The head of Virgin is expected to support a powerful business and industrial consortium if it wins the bid to take over the vessel later this year when it is decommissioned after its last mission to Hong Kong to mark the ending of British rule over the colony.
The state rooms used by the Queen and the Royal Family would be open to members of the public for the first time, with tourists paying about pounds 7.50 a head to visit Britannia.
The Queen has told the Government she intends to remove gifts and personal possessions, but most of the rooms will be left intact, and the bidders are proposing that some items, such as gold cigarette lighters, will be replaced with replicas by the original makers.
David Grocott, a spokesman for the consortium, which includes a number of top British companies, said it would be "putting the use of Britannia back to the people".
Britannia could be used for weddings, yacht-club functions regattas, and teaching young people about seafaring. "It is a world-class tourist attraction, but it is also an opportunity for the British public to see the royal yacht at close quarters. Many people regard it fondly, and it would be a great boon to have it at Greenwich for the millennium celebrations," said Mr Grocott.
Rival bids have been made to moor the royal yacht at Portsmouth but the consortium headed by Swift International, one of the front runners, is basing its bid on Greenwich as an international maritime centre, and site for the millennium exhibition.
It would cost about pounds 10m to site the vessel at Greenwich, including an application to the National Heritage commission for pounds 2.3m funding from the National Lottery. It would cost an estimated pounds 50,000 to tow Britannia from Portsmouth, in Hampshire, to Greenwich, in south-west London.
Some potential bidders were put off by the cost of the upkeep of the royal yacht, which could be increased if the mooring was on the tidal part of the river, where the bottom of the vessel would rest in the mud. The consortium is planning to moor the yacht at the Victoria deep-water terminal, on the Greenwich peninsula, near the site of the millennium exhibition; the meridian line would run through the ship.
Mr Grocott said that Portsmouth had many rival attractions, including the Victory, Nelson's flagship, and a naval museum. "We have estimated that the cost for an average family to visit all the historic ships at Portsmouth would be over pounds 100.
"Mooring Britannia there would actually mean some of the other attractions in Portsmouth would lose out."
The final decision on bids will be taken after the general election, but the battle will continue over the fate of the Government's plans for a pounds 60m replacement yacht to act as a focus for Britain's export and diplomatic drive abroad.
The Tories have ruled out private finance for building a new Britannia, but Labour has made it clear that it would not go ahead with a scheme financed by the taxpayer, given the financial demands for other projects, including hospitals and schools.
There have been suggestions, denied by ministers, that the Queen opposed a yacht financed by private sponsors. Unless there are strong objections, a Labour government may go ahead with private finance for the yacht.