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Mr Walsh also blamed politicians for being "afraid" of tackling the issue of airport capacity.
He said: "I think it is fear on the part of politicians. They are afraid to tackle tough issues.
"It (expansion) has been kicked into the long grass and I think it will be sitting there for a considerable time."
He envisaged that there would still be only two runways operating at Heathrow even as late as 2050:
"New runway capacity is required, but I don't believe that capacity will be provided....This issue is too difficult for politicians and governments to deal with. We are positioning our business on the basis that there will be no expansion," he added.
The head of British Airways' parent company, Willie Walsh, has warned that Heathrow will soon be overtaken by Dubai as the world's biggest international airport.
Speaking to the House of Commons Transport Committee, Mr Walsh said that the Middle Eastern airport had grown massively over the last decade - and could outstrip Heathrow "within two to three years".
In 2001, Dubai was the 99th biggest international airport in the world. By 2001 it was in 13th position and by 2011 it was fourth, he said.
British Airways chief executive Willie Walsh will face a transport select committee today.
He will discuss the Government's aviation policy, and is expected to give his thoughts on the controversial idea of a third runway at Heathrow Airport.
Walsh is also the Chief Executive of International Airlines Group.
Heathrow's Chief Executive has told a committee of MPs that the airport must be allowed to expand to boost UK business. Even though other airports around London have spare capacity, Colin Matthews argued that long-haul airlines prefer Heathrow because it can handle more transfer passengers.
He says the airlines can only fill long-haul flights if the departure airport is a hub with lots of short-range links allowing passengers to go there and transfer. He warns that if Heathrow does not expand, airlines will use airports like Paris or Amsterdam instead.
The bosses of London's four major airports are to give evidence to the Transport Select Committee, as it investigates the Government's aviation policy.
Colin Matthews, chief executive of Heathrow; Stewart Wingate, chief executive of Gatwick; Glyn Jones, managing director of Luton and Nick Barton, managing director of Stansted are due to be questioned this afternoon.
Campaigners opposed to airport expansion are also due to appear. Tim Johnson, director of Aviation Environment Federation and Chris Crean from Friends of the Earth are two of the organisations who'll face MPs questions.