LONDON — PRIME Minister Margaret Thatcher has won the backing of Britain's ruling Conservative Party to continue as leader - but she has also received a warning that if she does not modify her political style and some key policies, support may begin to crumble in coming months. That is the outcome of the first Tory leadership contest since Mrs. Thatcher took control of the party 14 years ago.
In the Dec. 5 vote, she beat off a challenge by a prominent backbencher by winning the support of 314 of the 374 Conservative members of Parliament eligible to vote. But this means that 1 out of 6 Tory MPs failed to support her - a result less satisfactory than the prime minister had been hoping for.
Sir Anthony Meyer, the Tory elder who acted as a ``stalking horse'' candidate to test the amount of enthusiasm for Thatcher's leadership, said afterward that he was ``happy'' with the result. He conceded that the prime minister had won by a wide margin, but suggested that she might still have to consider resignation in the next year or two.
Thatcher, whose supporters had applied exceptionally heavy pressure to Tory MPs to vote for her, said: ``I am very pleased with the result.'' Leading Conservatives however privately conceded that Sir Anthony had done much better than expected.
Sir Anthony's challenge was based largely on criticism of her attitude toward Europe which he described as ``narrow, unimaginative, and bad for Britain.''
In a speech in Brussels after the Malta summit, President George Bush appeared to side with European leaders who regard Thatcher's European policies as unhelpful and obstructive.
Beyond London, in provincial areas where the Conservatives are generally strong, the immediate effect of the leadership contest outcome has been to sooth jangled party nerves.
``We can now look forward to the next general election in the virtually certain knowledge that Margaret Thatcher will be our leader at that time,'' said the party chairman of a Tory-held constituency in the Surrey ``stockbroker belt.''
The opposition Labour Party, however, believes Thatcher will remain vulnerable to pressures in her own party and unable to recover the strong public support nationwide she used to enjoy. The Conservatives are trailing Labour by 10 to 12 percentage points in the polls.
A Labour Party spokesman said after the leadership vote: ``She has beaten Anthony Meyer. We didn't expect anything else. But she and her party are well behind in public esteem. We will make certain things stay that way.''
Domestically, leading figures in the Cabinet have served notice that they expect the government to support moves for greater European integration, despite Thatcher's personal reservations.
The deputy prime minister, Sir Geoffrey Howe, is continuing to adopt a more enthusiastic approach to European unity than Thatcher. He has the support of the newly appointed foreign secretary, Douglas Hurd, and, it is believed, the new chancellor, John Major.
On Dec. 2, Sir Geoffrey spoke with approval of full British membership of the European Monetary System, which Thatcher opposes, and forecast that Britain was likely to join before the next election - an outcome which the prime minister is resisting.
In years past, Thatcher would have been able to order a halt to such expressions of independent view by senior ministers. Now she cannot.
This weekend Thatcher is due to travel to a European Community summit in Strasbourg. Her officials say she will continue to resist moves toward economic and monetary union. If so, she is likely to find herself in a minority of one among the 12 EC leaders.