But if John Major heeds their message to escalate the "beef war", he could be putting his Commons majority at risk, as the Tory MP, George Walden, has warned he would have to consider his position in that event.
Tory voters overwhelmingly support the Prime Minister's campaign to disrupt Brussels business, with 77 per cent saying he was "right" to embark on it. One in five (19 per cent) said it had hardened their determination to vote Tory again. Even when opposition supporters are included, there remains firm support for the Government's stance, with 54 per cent of the whole sample supporting the campaign to frustrate EU work, and only 33 per cent opposing it.
Most Tory supporters (62 per cent) said they would ban German imports if the beef ban stays. Half of Tory voters want to threaten to pull out of the European Union altogether.
Public opinion as a whole is evenly split on whether to retaliate against German imports, with 47 per cent in favour and 45 per cent against. And voters generally are only narrowly opposed to the idea that, if the ban stays, Britain should threaten to withdraw from the EU: that option was opposed by a margin of 47 to 43 per cent.
Those findings imply that, while Mr Major's battle with Brussels may be popular with the core Tory constituency, it may not help improve the Government's popularity among floating and other voters.
However, the scale of anti-EU sentiment revealed by the poll was described as "worrying" by Mr Walden, who on Sunday threatened to bring the Government down if it escalated the beef war. He said: "This makes it all the more important that anyone who has doubts [about the Government's strategy] should speak out. It is possible to take a strong line without misleading people as to what can be achieved and what the options are. There is no option of forcing the Germans to eat our beef. There is no option of leaving Europe."
The Government came under swift pressure yesterday after Roger Freeman, the Public Service minister charged with eradicating BSE, backed off the idea that a timetable for lifting the beef ban would form part of talks with EU partners. He said on BBC radio: "We have said we want a framework. We don't want a detailed timetable that inevitably by a certain date certain things must happen."
John Redwood, last year's Tory leadership challenger, countered: "Farmers and persons in the meat business would expect a timetable for the remaining threat to their jobs and businesses to be lifted before the Government resumes normal co-operation with Europe."
Jacques Santer, President of the EU Commission, has ruled out a timetable for lifting the ban. The ban on gelatin, tallow and semen will be lifted next week, he said, but ministers admit the main ban on beef exports may still be in place at the end of the year.
Mr Major will enter dangerous political waters if there are no signs by the end of the month that the main ban will be be lifted. He has made it clear that he would not countenance any action - such as banning German imports - which is illegal, but that is unlikely to be popular with Tory right-wingers.
Mr Major was backed yesterday by David Hunt, the former minister who is leading a concerted loyalty drive and claiming a clear majority of Tory MPs - 200 out of 326 - under the Conservative Mainstream banner. "When the Prime Minister gives a lead, he should be given support, and much more loudly," Mr Hunt said. "But there can be no question of illegality".
Tory right-wingers have, however, warned Mr Major against "leading them up to the top of the hill and back down again". Even the centrist David Wilshire, MP for Spelthorne, said yesterday: "If he starts compromising, all is lost. He has no choice but to see it through."
In a newspaper article today Mr Walden compares Mr Major to "the man who thought he was leading the crowd and looked round to find they were chasing him".
Robin Cook, Labour's foreign affairs spokesman, is expected to say today that the Government's aim should be a complete lifting of the ban by the Florence summit on 23 June.
NOP interviewed by telephone a representative quota sample of 1,005 people aged 15+ on 24 and 26 May.
More poll findings tomorrow: Is Blair ready for government?
British voters show their anger at Europe
(All figures are percentages. Tory, Lab and LD refer to respondents' usual political allegiance)
Is the Prime Minister right or wrong to disrupt EU business to try to get the ban lifted?
If the ban is not lifted, do you think Britain should retaliate by banning imports from Germany?
If the ban is not lifted, do you think Britain should threaten to withdraw from the EU?