Campaigners are rejoicing after winning an “historic victory” over BAA as the air operator finally withdrew its planning application for a third runway at Heathrow.

BAA’s decision this week marked the end of a six year battle by residents, eco-activists and councils. It came after the new coalition Government scrapped the plans in a joint policy agreement on May 12.

Villagers in Sipson, which would have been demolished to make way for the project, were jubilant this week, and high-profile campaigners also expressed their joy.

Zac Goldsmith, MP for Richmond Park, said: “BAA’s announcement can be seen as a final victory against the proposed plans.

“This is good news for us all, and in light of an increasing skepticism of political promises, I hope it goes some way to rebuilding trust between politics and people.”

Mary Macleod, MP for Brentford and Isleworth, said: “I am delighted that BAA have stopped working on the planning application for a third runway. I listened to residents when they said they did not want an increase in flights, noise and pollution and campaigned against the third runway.

“David Cameron and I have now fulfilled our election promise. We have said no to a third runway at Heathrow. I will continue to work with local residents on issues that really matter to them, in the months and years ahead.”

Councillor Jagdish Sharma, leader of Hounslow Council, said: “This is great news for people living on both sides of the airport. An additional runway with all the noise and pollution would have been devastating for their quality of life.”

He added: “Now that the runway battle is over we will be pressing for tougher controls on noise and air pollution around the airport.”

Leading environmentalist John Stewart, chairman of campaign group Hacan, was named by the Independent on Sunday as the most effective green activist in 2008 for his work representing residents living under Heathrow’s flight paths.

He said: “BAA has bowed to the inevitable. It is a major victory for the opponents of a third runway. We have won an historic victory.

“We have always argued that a new runway was bad for the environment and was not needed for the health of the economy.”

Geraldine Nicholson, chairwoman of the No Third Runway Action Group, added: “All our hard work has paid off. We are now determined to make sure we never ever go through this again.”

BAA said it still believed expanding Heathrow was important for economic growth, but both the Conservative and Liberal Democrats opposed a new runway.

Colin Matthews, chief executive of BAA, said: "We recognise the importance of government policy in a matter as significant and controversial as runway capacity.”

But he added: “Heathrow plays an important role for the UK and supports thousands of jobs. We continue to believe that new capacity would strengthen the UK's trading links with the global markets on which our economy and our competitiveness depend."

The Government’s 2003 aviation white paper outlined plans for Heathrow expansion along with an extra runway at Stansted, which has also been scrapped.

The Tories preferred improved rail links to and from Heathrow, along with a new high-speed line from London to Scotland.