Prime Minister James Callaghan announced last night that his minority Labor government would carry on and there will be no general election in Britain this fall.

Callaghan's brief address to the nation shocked most pundits and politicans who had confidently predicted a vote on Oct. 5. Opposition Conservatives had been so sure that their canvassers began handing out leaflets in London neighborhoods yesterday morning, hours before Callaghan spoke.

Callaghan, 66, who clearly has enjoyed his 29-month stay at 10 Downing Street, is in no hurry to risk losing his lease. The political and economic arithmetic here made the outcome of any election now highly uncertain. The polls show the two major parties running neck and neck.

The chances now are that Callaghan will decide to call an election sometime next spring. A vote must be held by October 1979, five years after the last election.

After Labor regained power here under Harold Wilson in 1974, the country endured three years of falling living standards, rapid inflation and rising unemployment. It is only this past year that those losses were recovered and inflation tamed.

Callaghan evidently wants to put as much space as possible between the lean and fatter years before he faces the voters. In addition, while he has put through tax cuts to take effect this fall, it will be another six months before they expand demand, output and jobs.

Finally, a new register of voters will appear in February. It will pick up many young Britons who have just turned 18 and many workers who have shifted their jobs and homes. Labor strategists figure a vote after the register is issued will add up to 12 seats to their total" - an important factor in a tight race.

The government could be brought down against its will in November when the House of Commons votes on the queen's speech, a state of the union address. Labor can now count on only 311 of the 632 votes in Common - less than a majority, but a mere 10 abstentions could save Callaghan and these should not be too hard to find.

Callaghan will look for them among the 13 Liberals, who had been in a pact with Labor and who face virtual extinction in any early vote; 11 Scot and thee Welsh nationalists, who want the government in power until referenda are held to give the ancient kingdoms a limited measure of self-government; and the 10 Ulster Protestants, whom Callaghan has been silently wooing by preserving a status quo in Northern Ireland that discriminates against Catholic employment.

Callaghan's minority status in Parliament means he cannot pass controversial legislation but that coincides with his centrist approach anyway.

In his four-minute speech over radio and television, Callaghan said an election now would not solve any of the nation's problems.

He singled out pay increases and inflation as particular areas that an election could not help. This was a telling defense against the attacks he can expect from Margaret Thatcher, leader of the Tories.

Many in the business community, natural Conservative voters, feared that a Thatcher victory now would inspire unions to press sharply inflationary demands. With Callaghan in office, businessmen can hope unions will show some measure of restraint.

A disappointed Mrs. Thatcher said last night that Callaghan "has made a mistake . . . against the nation's interests. He has lost his majority and with it the authority to govern."