Mr Flynn will table compromise proposals at a meeting of officials on Monday in an attempt to reach a breakthrough. He is writing to Tessa Jowell, the public health minister, urging her to reverse Britain's position before a council of health ministers in Brussels on 4 December.
Labour MPs were furious when Ms Jowell told a backbench meeting at the Commons that a deal may not be reached on 4 December, and could be put off until April next year, when Britain would hold the presidency. MPs said she told them: "It could be 4 December, it could be April, it could be never."
Roy Hattersley, who has accepted a Labour peerage, last night said the "fiasco" over Labour taking pounds 1m from Bernie Ecclestone, the Formula One chief, was symptomatic of Tony Blair's attempts to find new friends in forging a consensus for the Labour government.
Calling for a clearer vision from Mr Blair in support of traditional Labour values, Mr Hattersley said in a Hansard Society lecture: "The Government would have avoided even the transient embarrassment had it been guided by a clear and consistent view of who its friends are and whose interests it most wanted to serve."
Mr Flynn's office said he was "dismayed" at receiving a letter last week from Ms Jowell announcing the British decision to demand the exclusion of Formula One from the European ban. "It came as a bombshell," a spokeswoman for Mr Flynn said.
Mr Flynn will press the Government to offer a compromise which could delay the introduction of a ban on sports sponsorship by tobacco companies. A delay of three years had been offered for most sports, but he is prepared to extend it. Officials will be meeting in Brussels on Monday to discuss a compromise formula before the ministers' meeting.
Britain is still formally sticking to its demand for a total exclusion of motor racing, but privately Whitehall sources said Ms Jowell was under orders to accept a 10-year delay as a fall-back position. That may be too long to satisfy Britain's European Union partners, said Mr Flynn's office.
Ash, the anti-smoking campaign group, is also appalled by Britain's position. Ash said the voluntary code had been shown as inadequate by breaches by motor racing teams at this year's British Grand Prix at Silverstone in July.
The code is supposed strictly to limit tobacco advertising at Grand Prix events. Ash complained to Comatas, the committee for monitoring agreements on tobacco advertising and sponsorship, that in one case the Marlboro red and white chevron was clearly visible on the Ferrari car. In another, the word "racing" was in exactly the same style of lettering as used to denote the Rothmans cigarette brand.
Comatas said the teams had been using these symbols for a number of years, but had agreed to change them for next season. However, it rejected two further complaints by Ash. In one it had said the Jordans car was advertising Benson & Hedges, and in the other it claimed the Williams car was advertising Rothmans.Reuse content