Britain's inflation rate dropped to its lowest level in 15 years last month, a major element in what Prime Minister Margaret Thatcher's government and the country's business community now believe is a broader economic recovery.

The prospect of an improving economy, coming at the end of Britain's worst recession since the 1930s, also has quickened the country's political tempo. A growing number of Conservatives are urging Thatcher to call a June election that would take advantage of her continued strength in the polls as well as the signs of economic upturn. So far, the prime minister has remained uncommitted on an election date.

The inflation figures released today showed an increase of 0.2 percent in March and a 12-month total of 4.6 percent, the lowest level since the spring of 1968. Economists predict that inflation will drop still further in April and May before increasing again slightly as effects of a recent decline in the value of the pound come to be felt.

Many other economic indicators--with the significant exception of unemployment figures--are also starting to improve. These include new orders reported by the Confederation of British Industry, sales of new cars and gross trading profits. The country's banks last week lowered the base lending rate to 10 percent.

After a meeting with West German Chancellor Helmut Kohl today, Thatcher welcomed the inflation report and said she and Kohl had agreed that "recovery was stirring" throughout the West. "We're not talking about enormous figures," she said. "We're talking about a soundly based, durable, steady recovery."

Some of Thatcher's backers in the business world are taking an even rosier line, at least as far as Britain is concerned. Speaking at the Confederation of British Industry's annual dinner earlier this week, its chairman, Sir Campbell Fraser said, "There have been false dawns in the past but there is no doubt that the serious people who make up this confederation are sensing a change for the better . . . .

"The long slow decline into mediocrity that seemed to be the modern industrial history of the country may have come to an end."

Buoyed by the economic news and her political advisers' confidence that she would win a June election handily, Thatcher is plainly relishing the speculation over a date and teasing her political opponents. Addressing the CBI, she recalled an old song, "Some say Maggie may. Others say Maggie may not. I can only say that when the time comes I will decide."

In Parliament that afternoon, when Denis Healey, deputy leader of the Labor Party, heckled her with the suggestion that an election in June, nearly a year before a ballot is required, would amount to a "cut and run," Thatcher retorted, with a taunting tone in her voice:

"Oh, the right honorable gentleman is afraid of an election? Afraid, afraid, afraid. Frightened. Couldn't take it, couldn't stand it." No, she added, "if I was going to cut and run I would have gone after the Falklands," a reference to last year's South Atlantic victory over Argentina.

From all accounts, Thatcher is genuinely undecided about the election date. She repeatedly has said she will make no decision until after her fourth anniversary in office, which comes in early May and coincides with elections for local offices around the country. A general election campaign in Britain lasts only three weeks, so Thatcher could announce in early June and still assure a voting date before the start of the summer holiday season here.

Her Cabinet is known to be divided among those who believe that an early election would produce a resounding mandate and those, generally among some senior members, who feel a date in the autumn would allow the economic picture to improve. Thatcher's personal preference had been to run the full length of her term--May 1984--but that is no longer the case. A late election, as one close Thatcher adviser noted this week, leaves ample chance for something to go wrong at the last minute.

Thatcher's predecessor as prime minister, Labor's James Callaghan, put his election off until the deadline and was badly hurt by a series of debilitating strikes in the final winter.

None of the economic forecasters predict a meaningful drop in unemployment, currently at 12.3 percent, because the size of Britain's industrial base has suffered so much during the recession. So whenever Thatcher chooses to run, she will have to persuade the electorate that in a second term, her fiscal policies, improved exports and higher productivity will put some of the country's 3 million jobless back to work.