Fresh from recent by-election successes and riding high in opinion polls, the two-party alliance that lays claim to an amorphous center in British politics has stumbled over a crucial issue in its quest for national power.

A long-festering disagreement between the Liberal and Social Democratic Parties over Britain's future as a nuclear power erupted with today's publication of a "joint" defense paper that one-half of the alliance leadership, former foreign secretary David Owen of the SDP, says does not represent his views.

Both alliance parties agree that Britain should not go ahead with plans to expand its independent nuclear deterrent with four new Trident missile-equipped submarines.

The $15 billion Trident program is the keystone of Prime Minister Margaret Thatcher's plans for nuclear modernization, destined to begin within the next several years as Britain's four Polaris submarines are phased out.

The SDP-Liberal dispute is over whether the alliance should commit itself to a cheaper, smaller replacement for Polaris, as Owen advocates, or a nonnuclear future for Britain after Polaris, a stance dear to the pacifist Liberals.

To resolve their differences, the alliance two years ago established a joint commission on defense. In addition to canceling Trident, the commission paper recommends strengthening the European side of NATO in its dealings with the United States, greater NATO reliance on conventional weapons, and pushing for arms control agreements.

The report leaves the question of replacing Polaris open, however. "Polaris does not need to be replaced now," it says. "No decision . . . can properly be made" without taking into account the status of arms negotiations, the cost of alternatives, and the opinions of Britain's European allies.

That position was designed to paper over the disagreement. But, in a series of speeches that have enraged Liberals, Owen has branded it "fudging and mudging" deserving of "a belly-laugh from the British electorate." Owen, who left the left-wing Labor Party five years ago and helped start the SDP out of concern over Labor's promotion of immediate and unilateral disarmament, believes indecision on defense will contribute to charges that the "so-called alliance" is a wishy-washy group of politicians who do not agree on much except their dislike of Thatcher and Labor.

Although the Liberals have not been in government since 1924, they are a longstanding party with firm traditions -- including a sort of unilateral pacifism that in the 1960s brought proposals to disband the British Army. Liberal leader David Steel has sought to move the party toward acceptance of Britain's role in the NATO military partnership.