The millionaire businessman is keen to win the right to take over the running of the lottery with a non-profit-making consortium from the current organiser, Camelot, which has been criticised for making excessive profits.
Labour yesterday made it clear that the party remains committed to allowing a non-profit-making organisation to take over the running of the lottery, if it can be financed more cheaply.
But senior Labour sources told The Independent that another organisation, such as Virgin, could only take over the contract from Camelot if its costs were lower.
Camelot won the contract partly because its costs were lower than competitors, including the Virgin consortium, but Camelot's pounds 1m a week profits could be squeezed by Labour applying a cap to its income from the lottery.
Camelot would also have to hand the pounds 6m a year interest on unclaimed prizes to the good causes funded by the lottery, Labour said.
However, the party is planning few dramatic changes to the National Lottery, if it wins power. It has ruled out suggestions that a cap should be put on the top prizes, such as the pounds 9m jackpot which was shared by three winners at the weekend.
Labour was attacked by Virginia Bottomley, the Secretary of State for National Heritage, after proposing to use lottery funds to pay for after- school clubs which would tackle the problem of "latch-key kids".
Labour's national heritage spokesman, Jack Cunningham, announced plans for a New Millennium Commission which would channel millions of pounds of lottery cash into projects for children and young people.
A top priority would be a network of after-school clubs - which Labour believes would be of particular help to single mothers - giving children the chance to do their homework, learn a foreign language or acquire computer skills.
There were also proposals to give local people much more say over the distribution of lottery cash. Small sums of money would be put into "community chests" which would be put under the control of panels made up from local business people, councillors and voluntary groups.
However, Mrs Bottomley accused Labour of planning to fund front-line education programmes with lottery money, breaking one of the main principles of the game, that its cash should not be used to fund basic government schemes.
She dismissed the plans as "a cocktail of political correctness" at the expense of those punters who enjoy an occasional flutter, and described the community chest scheme as a ploy to let Labour councils get its "sticky fingers" on the lottery billions.Reuse content