Lord Parkinson, the Thatch-erite former chairman of the party, told GMTV's Sunday programme that Mr Clarke had "offended a broad swath of the party by his rather cavalier attitude to people whose views don't agree with his, particularly on the subject of Europe.
"And there is a feeling that he held the last government to ransom - a feeling that is widely held, and that may at the end of the day count against him. I don't think he should be leader."
But Sir Leon Brittan, vice-president of the European Commission and a former Tory cabinet minister, told the same programme: "There's not the slightest evidence, and it's untrue, that Ken Clarke lost the election for the Conservatives."
He said: "If during that election we'd focused entirely on the economy, we'd have done very much better than we did focusing on the whole question of Europe."
Mr Clarke, he said, had done a tremendous job as Chancellor and it was "farcical" to suggest, as Lord Parkinson had done, that he would be too old to be prime minister in five years' time, when he would be 61.
"He has got tremendous flexibility of approach. He has the stature, the experience, and the common touch and those are a pretty formidable set of combinations," Sir Leon said.
It also emerged yesterday that Mr Clarke might yet look forward to an endorsement by Michael Heseltine, though the open support of John Major is more unlikely.
But many Conservative MPs still doubt whether Mr Clarke can come through to win. Like John MacGregor, contender in last week's election for the backbench 1922 Committee chairmanship, Mr Clarke is expected to be ahead on the first ballot - but with insufficient votes to establish a momentum for further rounds. If he cannot then pick up support from other challengers for the leadership, winning the necessary 83-vote majority of the MPs who are entitled to vote, MPs will quickly begin to switch to other candidates, such as William Hague or the dark-horse contender, Peter Lilley.
Mr Clarke's campaign was yesterday boosted by the public endorsement of Sir Bryan Nicholson, former president of the Confederation of British Industry. In a letter to selected Tory MPs, Sir Bryan warned that choosing a right-wing Euro-sceptic as leader would damage the party's relations with the business community and risk a long stay in opposition.
With Mr Clarke being seen as the Tory version of Denis Healey, Labour's former Chancellor, Sir Bryan cautioned Tory MPs against taking the "Michael Foot option" of abandoning the centre ground, as Labour had done after its defeat in 1979.
The problem with such endorsements is that Sir Bryan has no vote, and limited influence on MPs who will form their own judgements.
But for those wanting a mix of Mr Clarke's left-wing background and a dash of Euro-scepticism, Stephen Dorrell yesterday offered the prospect of outright opposition to British membership of the European single currency, with the possibility of a withdrawal of the party whip from rebels who broke party ranks to support membership.Reuse content