David Cameron has come under increasing pressure to break a coalition Government agreement and support a third runway at Heathrow.

Tim Yeo, a Conservative backbench MP, publicly challenged the Prime Minister to back the idea this week, goading him to show whether he is a “man or a mouse”.

Justine Greening, the Transport Secretary, said she remained concerned about increased noise and pollution and would find it difficult to remain in the cabinet if the Government reversed its aviation policy.

Environmental campaigner John Stewart, of Hacan Clearskies, said: “I think that behind this is a concerted attempt to persuade Cameron to move Justine Greening in the forthcoming reshuffle.”  

It comes amid speculation that Mr Cameron will also appoint Housing Minister Grant Shapps, who supports Heathrow expansion, as the new Conservative Party chairman.

But Mr Stewart, who represents residents living under Heathrow’s flight paths, said lobbyists’ attempts to pile pressure on Mr Cameron to break the coalition agreement appeared to have failed.

Nick Clegg, the deputy Prime Minister, said: “We're not going to give the go-ahead to the third runway at Heathrow because we said very clearly as both parties that we wouldn’t do so, so we’re going to stick to the coalition agreement.

“But that doesn’t mean we’re going to stick our heads in the sand over the aviation debate about capacity in this country and how do we make sure we have those proper connections to economies in Asia and Latin America which are important to our own prosperity and we’ll make sure we look at that.

“But there are lots of ways of doing that and we shouldn’t just lurch to one solution because one individual MP was to say so.”

Miss Greening, MP for Putney, joined Richmond politicians in campaigning against Heathrow expansion before she became a minister.

But some Conservative MPs argued the country needs a new runway at Heathrow to boost trade.

Mr Yeo, a former environment minister, told the Daily Telegraph: “The Prime Minister must ask himself whether he is man or mouse.

“Does he want to be another Harold Macmillan, presiding over a dignified slide towards insignificance?

“Or is there somewhere inside his heart - an organ that still remains impenetrable to most Britons - a trace of Thatcher, determined to reverse the direction of our ship? Let’s go for it.”