In an interview with The Independent, which is certain to inflame the debate over party funding, Mr Branson told of a "bizarre" invitation to dine with the former prime minister John Major when the lottery contract was up for grabs.
During the interview, Mr Branson also described in detail how hints were regularly dropped that he would receive "favours" - possibly honours - if he made a donation.
Mr Branson received the dinner invitation via a senior party fundraiser who, during a telephone call, claimed to be "close to the director-general of Oflot" - the lottery regulator.
He said: "I had this bizarre call during the process of the lottery just before the decision was made. It was from a senior fundraiser for the Tory party who asked if I wanted to have dinner with a senior person in the party."
Asked whether that figure was Mr Major, Mr Branson confirmed it was. He continued: "I wrote back and said I did not think it was a good idea. I felt it would be invidious at that time. It was an unnecessary call.
"There was something else during the conversation [from the fundraiser] when I was told that the caller knew the director-general of Oflot very well. I was uncomfortable with that." However, Mr Branson said he felt the fundraiser, whom he refused to name, was acting without the knowledge Mr Major.
"I like John Major," he said. "I do not think he would have behaved like that. I thought he was being used."
There was widespread surprise four years ago when Mr Branson's non-profitmaking lottery bid lost out to Camelot. The Virgin tycoon revealed last year how Guy Snowden, chairman of GTech, part of the Camelot consortium, had offered him a bribe to drop out of the race, but he famously refused. He won a libel case against Mr Snowden in June this year.
Mr Branson, 47, said he was regularly offered hints of honours in return for donations. "It was fundraisers who approached, never ministers - they always put people between them," he said.
Asked whether he had ever been explicitly offered a knighthood or another honour, Mr Branson replied: "It was never that clear cut. Everything was done by innuendo. It was made clear that if I scratched their back they would scratch mine.
"It was made clear that either you were a friend of the party or you were not a friend of the party ... Obviously, friends would benefit. Clearly donating was important."
Mr Branson is arguably Britain's most successful businessmen but he has never been honoured - even though he is expected to be recognised within the next couple of years. Labour turned down his nomination by the Tory leader, William Hague, for the last New Year's Honours List.
Mr Branson's book, Losing My Virginity: The Autobiography, is published next week, but he said yesterday that he could not recall whether he had named the fundraisers who hinted at favours.
"Hopefully, the new Conservative Party will show they are above this kind of thing," he said. "Whichever party is in power, they get the money and they do not want to change the system, but it has to be changed."
He said he believed state funding of parties should be considered. "At the very least, all donations should be instantly published," he said.
A spokesman for the Tory party said: "The Conservative Party never accepts donations with strings attached and has never done so."
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