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.
The chief executive of British Airways' parent company has attacked the government for refusing to expand Heathrow. Willie Walsh believes expansion is needed to connect with Asia. He said: "It's a nonsense to say that British business can be competitive if we can't fly to these destinations."