An increasingly bitter battle for control of the demoralized British Labor Party has hampered its opposition to Prime Minister Margaret Thatcher's Conservative government and increased interest in the formation of a new centrist party here.

The conflict, which could force a significant change in Britain's political alignment, pits the ascendant left wing of the Labor Party, led by former Cabinet minister Tony Benn, against the party's tottering centrist leadership of former prime minister James Callaghan.

The leftists are trying to push Labor toward more militantly socialist policies to offer voters a clearer alternative to Thatcher's free market philosophy rather than Callaghan's support of a mixed economy welfare state. Benn also wants to wrest the party leadership from a number of centrist contenders when Callaghan, 68, decides to retire.

Alarmed by what appears to be the polarization between Benn on the left and Thatcher on the right, several former Labor Party members are trying to launch a new, centrist Social Democratic Party to be headed by a former Labor deputy leader, Roy Jenkins.

Jenkins, who has served as the top civil servant in the European Common Market for the past four years, has repeatedly argued in favor of such a new party and hinted that he might be available to lead it when he completes his term at the Common Market office this year.

"We have just witnessed a major lurch to the left in policy making," Jenkins said recently in describing a special Labor Party conference dominated by Benn's people. "The divide within the Labor Party on a whole series of issues at the present is too deep to be bridged."

There is considerable skepticism in political circles here, however, about whether a major new political party can succeed. Questions have also been raised about how a new party would relate with the existing centrist Liberals, who have been perennial also-rans in postwar British elections. Liberal leader David Steel said he would be interested in cooperating with a Jenkins-led centrist party in future elections.

But leading Labor centrists who would have to be wooed to the new party to attract sufficient public support remain hostile to the idea. Former Labor Cabinet member Shirley Williams, for example, said such a new party would have no real backing or principles of its own. She added that the speculation about a new party is preventing the Labor Party from combating what she called the "destructive" policies of Thatcher's government.

She and other centrist contenders to replace Callaghan as Labor's leader want to expand Britain's welfare state while maintaining a mixed economy and active membership in the Atlantic Alliance and the European Common Market.

But Labor's sound defeat on that platform last year and Thatcher's attempt to steer the country completely away from socialism have embroidened the leftists to put forward their own policies.

Led by Benn's denunciation of Callaghan's "welfare capitalism," the leftists made their manifesto clear to a sympathetic audience at a recent Labor Party conference. They want to increase government ownership of business, encourage economic redistribution, take Britain out of NATO and the European Common Market, ban nuclear weapons on British soil and block imports that threaten British industry.

"We want a [future] Labor government as dedicated to carying out our policies as Mrs. Thatcher is to carrying out her policies," said Eric Heffer, a leading left-wing Laborite in Parliament.

Callaghan defended his record while maintaining his usual above-the-battle detachment. He smiled and said he was willing to let "a thousand flowers bloom" in the party.

But the courtly Callaghan -- still Britain's most popular politician -- has refused to say when he might relinquish the party leadership. This and his refusal to silence the ideological debate has appeared to exacerbate the power struggle among those who want to succeed him.

The contender rated to win out despite his advancing age is former chancellor of the Exchequer Denis Healey, a burly, brusque, infighter on the party's right wing. He has called the insurgent leftist "toy Trotskyites."

Benn, a pipe-smoking, soft-spoken former journalists who often has been called the party's "philosopher king," commands the intellectual respect but not the undivided loyalty of Labor's left wing.

His aristocratic background -- born Anthony Wedgwood Benn, he renounced a peerage that would have forced him into the House of Lords -- and participation in past centrist Labor Party Cabinets have not been forgotten by some of the most radical leftist constituent leaders.

The struggle for control of the party will not be resolved before the annual convention this fall. If Callaghan does not announce his retirement this autumn, the leftists vow to force a leadership election in November.