The map - published on a new campaign website supported by MPs including London Mayor Boris Johnson and Zac Goldsmith - suggests the airport's noise footprint would stretch some 30 miles from Bracknell in the west to Rotherhithe in east London - affecting more than a million people.
However, Heathrow, which claims it could reduce the number of people currently affected by noise even with a new runway, said the map was "inaccurate" and "unhelpful to local residents".
Richmond MP Mr Goldsmith launched the map at the House of Commons on Wednesday (June 17), alongside Mr Johnson and Putney MP Justine Greening.
"Implacable opposition to Heathrow expansion stretches from the affected boroughs to the very heart of government, and as countless hundreds of thousands of new residents are made aware of the threat they face, the campaign can only grow," said Mr Goldsmith.
"We have won the arguments on pollution, congestion, cost and competition, but the bottom line is that politically Heathrow expansion is undeliverable."
The map, based on the predicted flight paths with a third runway, is available to view at www.heathrowflightpaths.co.uk.
Mr Johnson, who was recently elected MP for Uxbridge & South Ruislip, said: "Zac Goldsmith has run a determined campaign to save London from the huge environmental damage a new runway at Heathrow would cause.
"The website he is launching today will bring home to Londoners how many more houses, schools and hospitals will be overflown if this undeliverable plan is approved. The Airports Commission must realise that, if it is mad enough to recommend a third runway at Heathrow, the backlash from Londoners will ensure it is never built."
There are currently 725,000 people significantly affected by noise from aircraft using Heathrow, according to figures from the European Commission.
Mr Goldsmith claims that figure would increase to over a million with a third runway, but bosses at Heathrow claim it would actually fall due to a combination of quieter planes and other changes like steeper flight paths.
A Heathrow spokeswoman said: "The map published today is inaccurate and unhelpful to local residents.
"The independent Airports Commission, made up of objective, technical experts has made its views clear - Heathrow expansion can take place while reducing the number of people impacted by noise.
"Heathrow has a new plan, one that has local residents' views and the environment at its core. And it will create up to 180,000 jobs and £211bn of economic growth across the country. That's why it has so much support this time from businesses, business groups, politicians, airports, airlines and a majority of local residents."
The Airports Commission is weighing up rival bids for expansion at Heathrow and Gatwick, is expected to make its final recommendation in the next few weeks.
However, recent reports have suggested the Conservative government may delay making its decision until the end of the year.