CONSERVATIVE Party stalwarts are saying John Major has until the autumn to prove he has what it takes to lead Britain - otherwise they will look around for somebody to replace him.
Dissatisfaction, most of it voiced privately, with the man who replaced Margaret Thatcher as prime minister in December 1990 reached new levels of intensity last week when Mr. Major's seemingly accident-prone government was hit by three new crises within seven days.
* The Labour Party opposition pressed home accusations that the Conservatives funded their party with millions of pounds from foreign governments. Major denied the charges but refused to publish his party's accounts.
* Michael Mates, minister in charge of antiterrorist operations in Northern Ireland, was forced to resign because of his support for Asil Nadir, a Turkish businessman who skipped bail in Britain and fled to Cyprus. Mr. Mates stepped down only a month after Major, in a bid to give the government a new lease on life, had sacked Norman Lamont, his unpopular chancellor of the exchequer. Mates, a former soldier, was a leading authority on security and antiterrorism.
* Michael Heseltine, a senior minister and the government's best speaker in the House of Commons, suffered a heart attack in Italy. He is thought unlikely to rejoin the Cabinet for months, if ever.
Of the three new problems Major faces, the most damaging promises to be allegations that his party gets much of its revenue from foreign sources. Members of Parliament normally loyal to Major are expressing concern about what one called a "sleaze factor" afflicting the Conservative Party. Publishing Tory income
During the weekend, several Conservative parliamentarians spoke privately of the need to publish the party's accounts. But Sir Norman Fowler, the Conservative chairman, said that was "not on the agenda."
He said 400,000 British pounds ($590,600) donated by Mr. Nadir would not be returned "unless it is proved to have been stolen." Lawyers for people who claim to have been defrauded by Nadir say they will sue the Conservatives for the money anyway.
In an attempt to turn the funding argument against the government's critics, Sir Norman said the Labour Party was financed by the trade unions. John Smith, the Labour leader, replied that his party publishes open accounts, whereas the Conservatives keep theirs secret. Two-thirds of Labour's 7 million British pounds ($10 million) annual income comes from trade-union donations.
Sir Norman said his party's income last year was 26 million, British pounds of which 18 million British pounds came from constituency associations. He refused to divulge the source of the rest, claiming that donors had "a right to privacy."
The Labour Party says much of the British pounds8 million of unaccounted for money came from foreign sources, including the governments of Saudi Arabia and Brunei. The London Observer reported June 27 that before the April 1992 general election the Conservatives received 500,000 British pounds from a group of business tycoons in Hong Kong.
The Sunday Times reported June 27 that the party accepted 1 million British pounds from a car dealer who has since fled to Switzerland to escape fraud charges.
The Conservatives deny these claims. `Unfairly attacked'
Major said June 26 that his leadership was being unfairly attacked by the news media, which was "concentrating on peripheral matters."
Sir Marcus Fox, chairman of the Conservatives' parliamentary committee, however, has criticized the prime minister's initial refusal to sack Mates or seek his resignation.
Dozens of Conservative backbenchers last week privately expressed concern about a lack of firm leadership from 10 Downing Street. The government's majority in the House of Commons is a slim 18 votes.
The prime minister's officials said Major was seething with anger at the criticism he has been receiving. One adviser claimed dissatisfaction was being whipped up by supporters of Lady Thatcher, who were still bitter about the way Major had displaced her in 1990.
As he struggles to reassert his leadership, Major is likely to be handicapped by the absence of Mr. Heseltine from the government front bench. Until his heart attack, Heseltine was the most forceful and articulate advocate of administration policy.
Heseltine's only rivals were Kenneth Clarke, appointed chancellor last month when Mr. Lamont was sacked, and Douglas Hurd, the foreign secretary.
Mr. Hurd is rumored to want to leave politics and take up an academic post. Mr. Clarke does not hide his ambition to become prime minister and is widely seen as the man the Conservatives are likely to turn to if the party decides to seek a new leader.