However, they told the audience of around 150 people they would not resign should their parties decide to support expansion at the airport. Instead, they said they would try to fight the policy from within the fold.
Both Labour and the Tories have said they will wait for the findings of the Airports Commission, which is weighing up rival bids for a new runway at Gatwick and Heathrow, before making a decision. The commission is expected to publish its recommendation in late May.
Green Party candidate Daniel Goldsmith and Liberal Democrat Joe Bourke both said their parties were clear in their opposition to a third runway, leaving UKIP's Richard Hendron as the only candidate to advocate an extra landing strip.
To a smattering of jeers from the audience, Mr Hendron said that speaking as someone who had lived under the flight paths for 34 years, he believed expansion was vital for jobs and investment in the area. He added that he thought a third runway was a "done deal" anyway.
Mr Goldsmith compared Ms Cadbury and Ms Macleod to two people on a rollercoaster, with no power to alter the chosen course of their parties on Heathrow, both of which he described as "ambivalent" about a third runway. He said the only way to register a protest against Heathrow expansion was to vote Green.
Despite the proliferation of anti-third runway badges among the audience, one voter was brave enough to declare his support for expansion. He said jobs in the area relied upon it and challenged candidates about why they had not said more regarding the impact on the local economy.
The anti-expansion candidates said they wanted Heathrow to remain as Britain's "premier" airport, though Mr Hendron claimed it would lose that status if it did not expand.
Mr Goldsmith said he didn't want Hounslow to be too reliant on a single industry as he believed aviation could go the way of shipbuilding and mining.
The meeting was organised by Brentford Chamber of Commerce, with support from NeighbourNet, the team behind BrentfordTW8.com. It was chaired by the chamber's president Suzie Betlem.
As well as Heathrow, rivals clashed over the impact of welfare cuts, whether an EU referendum should be held and possible changes to foreign aid, among other issues, during a sometimes heated two-hour debate at the church.
Below is a summary of what they had to say:
Marilyn Bater, secretary of Hounslow NUT (National Union of Teachers), said it was "shameful" that 3.5m children in the UK are being brought up in poverty.
She said teachers told her they were bringing food into class for students who would otherwise go hungry, and she demanded to know what candidates would do about the situation.
Mr Bourke said the coalition government had introduced free school meals for infant pupils and free pre-school childcare.
He claimed the economy was the "biggest driver" of child poverty and the coalition's work to improve the country's finances was beginning to "bear fruit", allowing child poverty to be addressed over the next five years.
Mr Goldsmith said we live in a "deeply divided and unjust society", where the richest 1% have as much as the bottom 55%.
He said the Greens would introduce a living wage of £10 an hour, which he claimed would go some way to eradicating child poverty.
Mr Hendron said exempting people on the minimum wage from income tax would help poorer families. He also said UKIP would make childcare for children under 12 exempt from tax.
Ms Macleod said the Conservatives' plan to raise the personal allowance - the income on which no income tax is payable - to £12,500 would make a big difference.
She claimed the best way to lift people out of poverty was to get them into work, and said unemployment in the constituency had fallen to 2% during her five years as MP.
She told voters she had visited the food bank Hounslow Community FoodBox, and said people were relying on its support for a variety of reasons, including domestic violence and delays in benefits being paid.
Ms Cadbury called her Conservative rival's claims about the food bank "unbelievable".
"All those people using that food bank do so as a direct result of the government's policies brought in since 2010," she said.
She added that many of those relying on the food bank were in work and many were on zero-hour contracts, with no idea how much work they would get day-to-day.
She said a Labour government would increase the minimum wage to £8 an hour, ensure all public sector workers receive a living wage and reduce the lowest tax rate to 10p, as well as freezing energy bills and bringing back tax credits (replaced under the coalition government by universal credit).
She claimed these measures would help working people who she said are £1,600 a year worse off than they were in 2010.
Michael Kelly asked what research the Conservatives had done to decide the coming term was the right time to hold a referendum on whether Britain should remain in the EU (European Union).
Ms Macleod said: "I think the people of Britain want a say. I've never had a say on Europe, and we've never had a proper say on whether we want to be integrated more and more into the EU as the years go by."
She added that the Conservatives would try to renegotiate the UK's deal with the EU before campaigning to remain in the union.
Mr Hendron, whose party has said it would hold an EU referendum as soon as possible, said: "When we joined the European project we didn't do so with the agreement to sign away our powers. We're now in a position where most of our laws are made in Brussels, which is unacceptable."
Mr Bourke said there was "no good reason" for a referendum at this stage. He said a referendum would only be needed if there was a change in the treaty which would involve any transfer of power from the UK government to the EU.
He said being part of the EU was vital for the success of the UK so it could compete with other trading blocks globally.
Mr Goldsmith said the Greens had "some issues" with the EU, which he felt was undemocratic and not in keeping with the party's belief in local decision making. However, he said it had been responsible for a number of good things, like the limits on air pollution.
He said the party would not stand in the way of a referendum but would "passionately campaign" to stay in the EU should one be held.
Ms Cadbury said David Cameron had done Britain "no favours" by allying in Europe with "extreme right-wing fascist parties". She claimed if the country left the EU it would be an "isolated, little inward-looking island" and millions of jobs would be put at risk.
She claimed Labour would ensure no government powers are lost to the EU without the consent of the British people.
Tax dodging bill
Candidates were asked whether they would support a tax dodging bill, making it harder for big companies to avoid paying their fair share.
Mr Goldmsith said "absolutely yes". He claimed the tax gap - the difference between what should be collected and what is actually paid - was £100bn. "There are a lot of loopholes which need to be tightened up", he added.
Ms Macleod said she couldn't commit to introducing such a bill within 100 days of a new parliament, as supporters of the measure have demanded, but said the Conservatives were "absolutely committed to doing more on this".
"We've probably gone further on tax evasion and avoidance than any other government. The tax discrepancy has fallen from 8.5% to 6.8% under this government," she added.
She said the Tories would increase the levy on non-doms - those who live in the UK but do not pay tax here on money earned overseas - and would keep pushing for international cooperation on taxation.
Mr Hendron said: "It's wrong for big companies to get away with paying virtually no tax. By leaving the EU we would end the practice of people paying tax in whichever state they think is most beneficial."
However, he criticised Labour's plans to abolish non-dom status as he said this would encourage non-doms to leave the country, reducing the total amount of tax collected.
Ms Cadbury said: "The simple answer is yes. I think it's remarkable for Ms Macleod to talk about what they're doing about tax avoidance and evasion when millionaires are being let off paying taxes at a phenomenal rate."
She said the Tories had cut funding for HMRC (Her Majesty's Revenue and Customs) so much it no longer had the tools to do its job properly and ensure people were paying the tax they owed.
Mr Bourke, who works as an accountant, said he felt it was vital tax loopholes were tackled and claimed the coalition government had done a lot to address the issue.
He claimed the true size of the tax gap was estimated by HMRC at £32bn, of which approximately £4bn was down to tax avoidance and £5.5bn to tax evasion, with much of the remainder down to proceeds from the country's black market, including prostitution and drug dealing.
A member of the audience noted UKIP's plans to cut foreign aid from 0.7% of the UK's spending to 0.2% and asked what the other parties would do.
Mr Hendron said: "Is it right when we have people in this country starving and old ladies who can't get the medication they need on the NHS that we give away so much money?" He claimed it was time to "put British people first".
Ms Macleod said that as an ambassador for the charity Action Aid she understood the importance of foreign aid and supported the 0.7% rate.
"The poverty you see in other countries around the world is absolutely shocking... We have a duty and responsibility to help these people," she said to applause from the crowd.
Mr Goldsmith said the UK should be acting to address deprivation in this country and across the world, where he said levels of poverty were "appalling". He said his party would increase the amount spent on foreign aid to 1%.
Ms Cadbury said the UK had a "moral duty" to support those around the world who are worst off. She also said many developing nations depended on remittances sent by people working in the UK to relatives in their native countries. She criticised banks in this country which have stopped catering for such financial transfers.
Mr Bourke said his daughter works for the charity War Child and there was never enough money for the important work it does overseas, often in countries which have seen UK military involvement.
"Providing foreign aid is not only the moral thing to do, I think it's in the UK's national interest to be participating with countries around the world to tackle these tremendously difficult problems," he added.
Veronika Weisweiller, of the Federation of Small Business, asked candidates what they would do to help small businesses and address the decline of local high streets.
Mr Bourke said business rates were the biggest issue for small firms, and business rate relief must be available to help struggling companies. He said local authorities had a big role to play in securing the redevelopment of their high streets, as is due to happen in Brentford.
Ms Cadbury said she would build the business partnership she started as Hounslow Council's lead member for economic development so she could address challenges and opportunities in the area with those affected.
She said Labour would cut business rates for small firms and create a British investment bank to lend money to small and medium sized companies.
She also claimed she had been responsible as a councillor for introducing 30 minutes' free parking in Hounslow.
She said a thriving town centre required offices and small businesses to be located there. She criticised the coalition government's decision to allow offices to be converted to homes without the need for planning permission, as she said was happening in Brentford and elsewhere in the borough.
Mr Hendron said UKIP would require all local authorities to allow 30 minutes' free parking on their streets, to which his rivals pointed out this was already the case in most of Hounslow, excluding Chiswick High Road.
He also said out of town developments should be replaced with social housing to "put the life back in our high streets".
Ms Macleod said: "Business rates are crippling small businesses. It's an unfair tax. What do businesses get for it?"
She said she had "nagged" chancellor George Osborne for a full review of business rates, which had already begun.
She pointed out that 9,400 new businesses had started in the constituency during the last five years and said if she were re-elected she would continue to fight for them.
Mr Goldsmith said better public transport and cycling routes were key to promoting small businesses and putting the heart back in the local community.
Hazel Dakers asked candidates what they thought was meant by affordable housing. She demanded facts and figures, not polemic.
Mr Hendron said he earned more than most young people as a barrister yet could still not afford a house in Brentford.
"I think it's a disgrace we have new developments like Kew Bridge going on the market first in Dubai before becoming available to local residents," he added.
Mr Bourke said the main issue in London was the lack of supply and claimed the only solution was a massive building programme.
Mr Goldsmith criticised the Right to Buy scheme, saying the social housing sold off over the last 20 years had not been replaced.
He said the Greens would bring half of England's 610,000 empty homes back into use and would build an extra 500,000 social rented homes to address the shortage of housing.
Ms Cadbury said: "When I last looked I think you needed a combined income of £70-80,000 to buy a one-bedroom at one of the flats on the market around here.
"The average first-time buyer is well into their 30s. Nick and I are rather concerned about how long we're going to have our boys under our feet."
She criticised the Conservatives' announcement that they would extend the Right to Buy scheme, enabling up to 1.3m more people in social housing to buy their homes at a discounted rate.
Ms Macleod accused Hounslow's Labour council of doing too little to address the situation.
"I keep saying to the council every development should have affordable housing in it but they don't always do that. They listen to developers instead," she said.
"Since 2011 this council has only built 98 council homes, despite having had £20m in the bank to pay for them."