Prime Minister James Callaghan's government last night lost what would once have been regarded as a crucial vote when opposition Conservatives forced the government to accept an unwanted extra $670 million in income tax cuts.

Times have changed in the mother of parliaments, however. Callaghan shrugged off the defeat and made it clear he neither intends to resign, nor plans to call a general election now. He will swallow the added tax reduction and regard it as just another episode in the life of a minority government.

Last night's vote was won by the Conservatives 312-304, with a rare united front of minor parties.

When the count was announced, Geoffrey Howe, the Tory spokesman for finance, called on the Labor government to resign. He was greeted with cool silence from Callaghan and his chancellor of the exchequer, Denis Healey.

In the past, no government could survive here if it lost a vote on the "budget," the odd British term for the tax side of the nation's finances.

But in the contemporary world, Labor will like it or lump it, being able to claim credit if the added tax slice creates jobs and blame the Conservatives if the pound falls or prices rise.

The affair illustrates that the era of two-party government with a decisive majority for one is over. Apart from the traditional minor third party, the Liberals, British politics now embrace nationalist groupings in Scotland and Wales plus sectarian Protestant and Catholic members from Ulster. They make it very difficult for either of the big two to gain unchallenged ascendency in Parliament.

A key factor in last night's outcome was the bloc vote cast against the government by seven Ulster Protestants led by Enoch Powell. They usually vote with Callaghan because Labor has preserved the status quo and its advantages for Protestants in Northern Ireland.

But once they were assured that the government would not fall over the tax issue, Powell and his party members could safely indulge in a pretense of opposition and vote with the Tories.

In the same way, 13 Liberals voted for the tax cut to dramatize their insistence that income taxes here are too high. But their leader, David Steel, had clearly indicated that he would not have voted against Callaghan on a motion of confidence, something that could topple Labor.

There is still one powerful political weapon - apart from patronage - in Callaghan's hands. He can pick the date for an election. The conventional view here is that he will call one in the autumn but his close advisers have been urging him to wait until the spring of 1979.

The new pattern of politics here gives Parliament a continental air. A multiplicity of parties means that a government must make formal or informal alliances with minority groups to stay in power.

That is just what Callaghan has done: a formal pact with the Liberals and an informal one with the Ulster Protestants.

In an odd way, too, the new share of politics also takes on an American appearance.Governments can no longer steamroller laws through a legislature where they enjoy huge and automatic majorities.

Instead, bills are amended in committees or, as in last night's vote, altered on the floor. All this makes it difficult for any government to move far from the center. The right-wing ideologues among Tories and left-wing ideologues with Labor are frustrated. The arithmetic compels politics of the center.

Last night's successful Tory motion slices a percentage point from the broadest tax bracket. This adds about 15 percent to the government's proposed tax reduction of $4.5 billion.

Healey has been hinting that he will make up the loss of revenue by hitting businessmen, Tory supporters, with stiffer taxes. He may, however, forget the whole thing and hope that it simply adds an extra stimulus to the large one he has already planned for the economy here.