New hard-line proposals, which were discussed by Cabinet ministers last week, are winning the backing of leading centre-left figures as well as Euro- sceptics. Stephen Dorrell, Secretary of State for Health, and Malcolm Rifkind, the Foreign Secretary are now seen as hawks on the subject.
The tougher approach may be revealed this week if a meeting of the EU veterinary committee on Tuesday fails to lift bans on British gelatine and tallow.
The heads of government meeting in Florence on June 21-22 is seen as a key point for a show-down with EU partners, unless progress has been made by then. The Cabinet is attracted to a strategy under which Britain would simply refuse to give in, digging in for concessions as Margaret Thatcher did over the EU budget in the early 1980s. This is seen as preferable to boycotting EU meetings - the so-called "empty chair" strategy.
One minister said: "There are different ways of diplomacy. You have to get the right balance of threat and inducement."
Another source said: "Stephen Dorrell is hard-nosed about it all. Malcolm Rifkind invites a greater range of options than his predecessor [at the Foreign Office], Douglas Hurd, and those options are inclined to be tough."
However Kenneth Clarke, the Chancellor, is resisting any hardening of the position which, he argues, could undermine Britain's international position in the long term - particularly if John Major's bluff is called. Earlier suggestions that the Government might retaliate by banning some European produce resulted in a humiliating retreat for the government.
However, the hand of those pressing for a tough new stand may have been strengthened by last Thursday's local election results, which were slightly better for the Government than forecast. Sceptics argue that some voters are blaming Europe, and not the Government for the beef crisis.
One right-wing Government source was enthusiastic about disrupting the EU Inter-Governmental Conference (IGC) in Italy. "What do we have to lose in saying: 'There is going to be no IGC until we have sorted this out?' " he said.
More significantly, anger with Brussels has spread beyond traditional sceptics. One pro-European ministerial source said: "If we do not get movement it will reinforce people's irritation about this, and that goes across the party, not just the sceptics who will be irritated anyway. That message will be conveyed at a very high level to foreign governments."
Downing Street is conscious of the risks attached to such a strategy, but Mr Major is determined not to repeat his experience at the last summit in Turin, where other leaders expressed sympathy and support for Mr Major's plight - but then failed to assist in lifting the beef ban.
A tough new line will anger some back-bench pro-European MPs. Quentin Davies, Tory MP for Stamford and Spalding, in an article for Sunday Business today attacks the Eurosceptics for blaming the EU for the ban. "The opposite is the case. The rest of the world took the initiative. The EU is not the problem. It is part of the solution."
Meanwhile John Taylor, deputy leader of the Ulster Unionists, will warn on BBC's On The Record today: "The Government cannot depend on the Ulster Unionists to keep them in power ... The Conservative Government abandoned strong support for the union between Great Britain and Northern Ireland. We no longer see it as a unionist party, and that being the case, the Labour Party is on a par with the Conservative Party as far as we are concerned."
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