As part of a survey conducted every two years to gather people's general views of services provided by Hounslow council, the local authority quizzed its residents on the major and controversial airport project.
Of the 1,207 residents interviewed, 44% said they support a third runway, which includes 18% who strongly support it, and 29% oppose it, including 21% who strongly oppose it.
A quarter of residents said they are neither for or against a third runway.
There were geographical differences with Hounslow Central showing 51% of residents support a third runway and 26% oppose it, while in Chiswick 31% were in support and 38% against.
In addition 46% of people think the council should support the cabinet's backing of the expansion, 25% think it should oppose it and 32% think the council should increase its work to reduce the impact of airport-related noise, pollution and congestion locally.
Commissioned by the council, Opinion Research Services carried out the latest poll between September 8, 2016 and October 18, 2016.
Councillor Steve Curran, leader of Hounslow council said: "Our position on Heathrow Airport, that is, that we would like to see a better not bigger airport, remains unchanged.
"As I've said before, the announcement that government now recommends expansion at Heathrow will have a huge impact on the residents and businesses of Hounslow.
"Our main concerns remain noise, pollution and additional congestion.
"We need to do more on these and so does Heathrow and the Mayor of London.
"We will continue to work with Heathrow on behalf of our residents and businesses, many of whom are employed directly at Heathrow or are part of the supply chain, to ensure the best possible outcome and to reduce any adverse effects of the government's decision."
Rob Gray, campaign director of pro-expansion group Back Heathrow, added: “It’s no surprise that more Hounslow residents support Heathrow expansion.
“Many will work at the airport and be glad that its future has been secured. Others will be looking forward to the new jobs and prosperity that will come to Hounslow from building a new runway."
The government will soon launch a consultation on airport capacity (the National Police Statement) and the council urges their residents to take part.
The survey also covers topics such as the local area and council satisfaction,communications and local democracy, residents' concerns, community safety and more.
Other highlights included a 3% rise in satisfaction levels with the exception of recycling collection services, refuse collection services and street cleaning which need to be improved.
Rubbish or litter lying around were the biggest antisocial behaviour concerns with 42% saying it is a very or fairly big problem, while 30% said the rate of repair to roads and pavements was extremely poor.
Residents also said they still find it harder than they should to get through to the council on the phone.
Councillor Curran added: “I am particularly pleased that, despite having had to make such large financial savings in the face of government cuts, we have been able to maintain high levels of satisfaction in many areas.
"Each time we do this survey we are reminded about areas where we need to do better. "
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