The club's 800 members - who include drivers like Stirling Moss and Jackie Stewart, the commentator Murray Walker and the former Chancellor Kenneth Clarke - stand to receive windfalls of around pounds 75,000 if Silverstone is sold. However, many of them are said to have been annoyed by an open letter they received from Nicola Foulston, the chief executive of Brands Hatch.
One BRDC member said: "The letter has just served to reinforce our opinion of the Brands Hatch bid. They will struggle to get the 75 per cent support they need."
In the letter, published in a motor industry magazine, Miss Foulston criticised a key element of a plan drawn up by bankers Dresdner Kleinwort Benson to restructure the club and create an executive to run the track. Miss Foulston said the plan would allow "an elite few" to block a majority decision.
BRDC members will meet on Friday to decide whether to proceed with Dresdner Kleinwort Benson's plan. Insiders say the plan would make it much easier for the BRDC to sell the track, which could fetch pounds 50m.
Miss Foulston has been spending the weekend at Silverstone in an apparent attempt to head off mounting opposition among members to a takeover by Brands Hatch.
Brands Hatch Leisure, the publicly quoted company which owns Brands Hatch, three other race tracks and the Daytona karting circuit, is one of a number of bidders to have approached Silverstone, which hosts the British Grand Prix.
Miss Foulston has put pressure on the BRDC by reportedly coming to an agreement with Bernie Ecclestone, the head of Formula One, to move the race to Brands Hatch if her bid for Silverstone is rejected. Whereas in her letter, she promised to keep the Grand Prix at Silverstone if the Brands Hatch Leisure bid is successful.
The loss of the Grand Prix would be a big blow to Silverstone, which generates most of its revenue from the race.
However, the BRDC seems certain to receive at least one firm rival offer - from John Lewis, a motor racing enthusiast and former chairman of Silverstone.Reuse content