The main demand is that the two carriers give up 168 slots a week at Heathrow, more than 90 per cent of the total number allocated to American, otherwise it would be referred to the Monopolies and Mergers Commission.
The conditions are a severe blow to Bob Ayling, chief executive of BA, who had insisted the two airlines should not be forced to give up any of their Heathrow slots.
British Airways said it was prepared to take reasonable steps to assist the introduction of additional competition at Heathrow, but Mr Ayling added: "The permanent, unconditional divestiture of slots is unprecedented and, if done, must be on the basis of fair market value."
However, Virgin said it would lobby the Office of Fair Trading to propose even tougher conditions. A spokesman explained: "We do not think the undertakings are enough to protect the interests of the flying public and we will be asking for it to be referred to the Monopolies and Mergers Commission."
The Government has in effect accepted arguments raised by some rival US airlines during their unprecedented lobbying effort against the alliance. United Airlines, the world's largest carrier, last night broadly welcomed the conditions. The announcement came as "open skies" talks between UK and US government officials concluded in London with little sign of progress.
The US negotiating team has already stated that it will approve the alliance only if the British government agrees to free up access to Heathrow for American carriers.
Mr Lang said competition must not be compromised by the tie-up, which would give the two carriers some 60 per cent of seat capacity on flights between the UK and US.
The link-up involves the airlines pooling revenues and facilities but does not include the two carriers taking shareholdings in each other.
The DTI accepted the OFT's advice that the alliance should give up 70 slots a week over the winter of 1997 and a further 28 slots a week the following summer. These would have to be given away permanently.
British Airways and American also have to lease out a further 70 slots by the winter of 1998, though these could be recovered later if competing airlines managed to buy up their own slots.