Runway capacity at is the greatest challenge Heathrow faces over the next decade, Willie Walsh, BA's ceo, said.
Speaking at the Aviation Club in London, he said: "The acute shortage of runway slots is the fundamental reason why Heathrow struggles - and T5 will bring no relief on this issue."
He said the London airport still had only the two runways it had 60 years ago while rival hubs
like Paris, Amsterdam, Frankfurt and Madrid had four or five.
He said the shortage of runway slots meant the airport served fewer destinations than it did 15 years and had fallen behind Paris, Amsterdam, Frankfurt and Munich.
He welcomed the UK government's support for a third runway at Heathrow "provided environmental safeguards on noise and local air quality could be met" and the start of consultations on the project in the next few weeks.
But while he acknowledged the concerns on global warming, Mr Walsh also laid out the economic benefits of aviation.
It is worth £12bn a year to the UK economy and supports 500,000 jobs, he said.
"Air transport is now as vital a part of the economic infrastructure as finance or IT.
"Without convenient access to good air links, businesses cannot compete effectively.
"Businesses need to meet customers. They need to meet suppliers and investors.
"In the case of the UK, that means we must develop Heathrow.
"We cannot hope to maintain London's status as a premier league business centre, supporting millions of jobs across the country, unless we provide world-class air links.
"If businesses can't find the connectivity they need from London, they will simply move elsewhere," he said.
Mr Walsh said a short, third runway at Heathrow would allow a 40-50% rise in the number of flights.
It would also add 75-80 new destinations, putting London on a par with Paris, Amsterdam and Frankfurt.
Earlier, Mr Walsh said the BA's move to Terminal five at Heathrow was crucial to the future of the airline.
BAA had already handed over the keys to the building and the first of the 70 trials needed before the scheduled opening next March had already taken place.
He also said an announcement would be made soon on the new fleet of aircraft BA plans to buy.
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