London — BRITAIN'S centrist parties have emerged from their annual conference season deeply divided, leaving the ruling Conservative and opposition Labour parties well placed to go on calling the tune of British politics. One center group ended its meeting at Blackpool bickering about what to call the party. The Social and Liberal Democrats - product of a 1987 merger between the old Liberal party and one wing of the more recent Social Democrats - had hoped to call themselves either the Liberal Democrats or just the Democrats. Instead, both titles will continue to be used.
David Owen, leader of the Social Democrat faction that refused to link up with the Lib-erals, has instilled unity into his party's ranks, but his group has only three seats in Parliament.
So the parties that hope to dominate the middle ground of British politics are in disarray.
Paddy Ashdown, leader of the Social and Liberal Democrats, expressed ``delight'' at the outcome of the debate about nomenclature. But there was more delight among Tory and Labour politicians who now say, with some reason, that the center parties are hopelessly divided.
This division removes any threat to Labour's position as the only effective opposition party, and reinforces Prime Minister Margaret Thatcher's dominance. The Labour party has been unable to dent the ruling Tories' popularity. Mrs. Thatcher's government enjoys a majority of some 100 in the House of Commons. The Tories, about to hold their annual conference, are in a buoyant mood.
Neil Kinnock, the Labour party leader, has tried to assert control over his followers. But he has been unable to prevent a radical group, led by Tony Benn, from challenging his leadership. Labour is also about to hold its annual conference, with a bruising leadership battle ahead.
For many decades the Tories and Labour have provided alternating governments, with the Liberals, a formidable force in the 19th and early 20th centuries, retaining a few seats. A decade ago, a group of moderate Labourites left their party to form the Social Democrats.
All that remains of their attempt to ``break the mold'' of British politics is a movement in two pieces - one, led by Mr. Ashdown, unsure of what to call itself; the other, led by Dr. Owen, so tiny as to require a political miracle to recover its credibility.