BAA, which runs Heathrow, ruled that Terminal 5 - which is still the subject of a marathon public inquiry - would be used solely by BA and its alliance partners if and when it was built.
Mr Branson, who is leading the fight to stop BA's plans to link up with American Airlines, the carrier with the largest turnover in the world, said the move would give BA an unfair advantage over other airlines.
"One has to ask whether this is a fair opportunity for customers to give a brand, spanking new facility to a monopolistic airline when all the carriers are paying for it," said Mr Branson, who intends to take the matter up with the Office for Fair Trading and the European Commission.
BAA says that its annual pounds 1.6bn revenue stream comes from three principal sources. More than pounds 500m of the company's cash flow is from its vast retail operations, another pounds 434m comes from charging airlines landing fees and more than pounds 200m is garnered from BAA's property portfolio.
Mr Branson's plea is also not an argument that BA accepts. Bob Ayling, BA's chief executive, said it had long been the airline's dream to offer customers "all of our services under one roof". "Today this dream moves one important step closer to reality," he said.
The company pointed out that it was also suffering from Heathrow's overcrowding. Recently, BA has moved its Latin American and Central African flights to Gatwick to free up slots at Heathrow.
The deal is conditional on BA leaving Heathrow's Terminal 1. Seen as a sop by other airlines, BAA is looking to hand over Terminal 1 to a mega-alliance of carriers including United, Lufthansa, SAS, Air Canada and Thai.
BAA's chief executive, Sir John Egan, said that BA's move was a key step in planning the Terminal 5 project. BAA said it would now discuss with other airlines just who should go where at the airport.
But Mr Branson said that BAA first floated the idea that BA might control Terminal 5 earlier this year. "When BAA told us that BA would have Terminal 5, we said that it was unacceptable without proper negotiations."
While all airlines and big business support Terminal 5, green groups and local councils oppose it. The public inquiry has run for nearly two years and will last for another 12 months. If planning permission is granted Terminal 5 could open in 2004.