That election is expected to be held next May, when the impact of tax cuts and improved economic prospects will have sunk in, according to Kenneth Clarke, the Chancellor of the Exchequer, in an exclusive interview with the Independent today.
One leading sceptic said last night that private doubt remained just as strong - but they had decided to maintain a public face of unity through to the election. The MP, one of the "Westminster Eight", the MPs who were stripped of the party whip after voting against the Government in November 1994, said they had agreed to back away from further confrontation because that could only help Labour and Tony Blair would be far more pro- European than Mr Major.
One Cabinet minister welcomed the decision, but he added: "The damage is already done."
Another Cabinet source said that it had been left a little late in the day, but Mr Clarke says in his interview that the polls on economic competence were improving quite rapidly in the Government's favour.
That view was bolstered by a MORI poll for the Times showing a three- point swing to the Tories since late May. The poll, taken between 21-24 June, showed an increase of four percentage points, to 31 per cent, in Conservative support, compared with May, while Labour dropped two points to 52 per cent, and the Liberal Democrats were down three points to 12 per cent.
Mr Clarke said the impact of tax cuts had only come into play over the past two months, adding: "If you can maintain that for 12 months ..."
That would clearly indicate a May election next year - and not the snap autumn election that has been predicted in some quarters. Mr Clarke said: "The policies have been set to continue the present improvement in the economic situation for some years, which I hope means we will be [a] slightly more popular government than we have been at times."
The Prime Minister had told him he would remain Chancellor through to the next election, and Mr Clarke added: "I was quite interested in what conditions might be like in late 1996 and early 1997, and I think it looks like a pretty good combination of circumstances coming up for late 1996 and early 1997."
The Euro-sceptic decision to back away from further confrontation follows two recent votes on backbench Bills, which were portrayed as humiliating setbacks for party unity. In April, 66 Tory backbenchers backed a call by Ian Duncan-Smith for curbs on the power of the European Court of Justice, and on 11 June, the total number of rebels rose to 78 on Bill Cash's Commons call for a referendum - with a dozen known sceptics missing from the vote.
One rebel said that with a total tally of about 90 sceptics - amounting to about half the Government's backbench strength in the Commons - they could bide their time until after the next election.
The common view among right-wing Tory MPs is that the party will suffer badly at the next election, with one former Cabinet minister talking of a halving of the number of MPs, to about 160 MPs.
Mr Major has repeatedly warned, at every opportunity, of the need for an end to damaging splits. He told this month's Welsh Conservative Party conference that he had had a "bellyful" of party strife. The Independent's sources have said that the informal peace pact was agreed over the past week at a variety of meetings of groups, including the sceptics.
While the first sign of a backdown came last week with Norman Lamont, the former Chancellor, talking of the need to "knuckle down" in the run- up to the election, the most significant evidence of a change of atmosphere was delivered in the Commons on Monday, when Tory MPs united behind Mr Major's Commons statement on the Florence beef deal.
One former dissident said it was a matter of common sense that if half a dozen MPs had attacked the deal - as they would have done in normal circumstances - the party would have "imploded". He said that the Prime Minister's credibility would have been destroyed, and his claim of victory would have been exposed for what it was; an empty claim.
Kenneth Clarke interview,