Two major Conservative donors say they may vote for the UK Independence Party unless leader David Cameron adopts a "much tougher" stance on Europe.
Mr Wheeler said he was torn between UKIP and the Tories
Stuart Wheeler said his vote was "in doubt" because the Tories had "not been nearly strong enough on Europe".
And former party treasurer Lord Kalms told the Daily Telegraph "the option remains open for me... to vote UKIP".
Meanwhile Mr Cameron told the newspaper that, rather than copying Tony Blair, he was following Mrs Thatcher's lead.
In an article he says: "I am learning from his (Tony Blair's) many and serious mistakes."
And he adds, for those party supporters who doubt if he is a true Tory, that his ideas are "the ideas that encouraged me as a young man to join the Conservative Party and work for Margaret Thatcher".
On Europe he says the Conservatives are promoting "a positive vision of an outward-looking Europe rather than an inward-looking EU obsessed with its own bureaucracy".
Mr Cameron says the past year has been one of "establishing the Conservative Party as the party of change, optimism and hope".
He writes: "I am proud that we are once again regarded by our fellow citizens as decent, competent and comfortable with modern world."
'Harm to country'
UKIP, especially since Nigel Farage became leader last September, has been seeking to woo Conservatives alienated by the direction of Mr Cameron's leadership.
Last week two Tory peers, Lord Pearson of Rannoch and Lord Willoughby de Broke, switched to UKIP, saying it was the "only party telling the truth" about Europe.
That gave the party its first Westminster representation.
Monday's Daily Telegraph quotes ex-Dixons boss Lord Kalms as saying the issue of Europe is "way above party loyalty... we will not be bound hand and foot to the Conservative Party over Europe.
"The issue is one on which the whole future of the United Kingdom depends. The option remains open for me, and Tories that I know, to vote UKIP."
Mr Wheeler, who made a fortune from a City spread-betting firm, has become the latest senior Conservative figure to publicly say he is being tempted by UKIP.
Asked about whether he might switch, he told BBC Radio 4's Today programme: "I'm in doubt at the moment."
He added: "I think Cameron's done a tremendous thing for the Conservative Party and I'd very much rather the Conservatives formed the next government, as I think they will, than Labour.
"Plainly, UKIP's not going to - and one side of me says I don't want to do anything to upset that.
"On the other hand, I think the Conservatives have not been nearly strong enough on Europe, which in many respects does a great deal of harm to this country - it has its benefits too - and I think it's terribly important that the Conservatives should announce that they're going to be very much tougher with the European Union."
But Shadow Foreign Secretary William Hague told BBC Radio 4's The World at One his party already had "tough" policies on Europe, although there was no chance it would advocate leaving the EU.
He said: "Anyone who is a member of the Conservative Party has a right to speak out.
"Donors have no more right than any other members. Our policies are not sold to donors."
Mr Wheeler, a long-time Conservative donor, gave £5m to help the party's 2001 general election campaign.