Unusually strong and widespread criticism of the harsh, high-tax budget for government presented Britain this week has embroiled Prime Minister Margaret Thatcher with the most threatening political controversy of her nearly two years in office.

Influential politicians in Thatcher's Conservative Party and business leaders have joined opposition politicans and labor leaders in condemning the budget for substantially increasing the tax burden on Britons while offering little inducement for recovery from Britain's worst recession in a half century.

A sizable minority in Thatcher's Cabinet is reported to be worried about the economic and political impact of the budget, which increases taxes to reduce a growing budget deficit and hold down government borrowing. The details of the budget, drawn up by Chancellor of the Exchequer Geoffrey Howe and the treasury under Thatcher's supervision, were revealed to the entire Cabinet only hours before Howe made them public in Parliament Tuesday.

The uneasy Cabinet ministers reportedly were surprised by the size of the tax increases, the paucity of relief for hard-pressed British business, and the likelihood that unemployment, already at a post-Depression record level, will rise even higher than expected. The dissenters, who want Thatcher and Howe to begin easing the squeeze on the economy, reportedly said at a Cabinet meeting today that they want an opportunity well in advance to review the next budget and any interim economic decisions the government makes.

The private misgivings of many dissenting Conservatives in Parliament were echoed in public by some of them, including senior backbencher Peter Tapsell, who also is a leading stockbroker. Tapsell said Howe's policies "are damaging the nation."

Vowing to increase private industry's pressure on the Thatcher government to loosen its economic policies, Raymond Pennock, president of the Confederation of British Industries, said the budget gave business "at best what might be described as a brushoff, and at worst a kick in the teeth."

The Conservatives, with a 43-seat majority in Parliament, are still virtually certain to approve the budget quickly in the House of Commons to avoid having the government fall. But those representing rural or industrial districts hit hardest by a particularly heavy increase in the tax on gasoline heavy increase in the tax on gasoline and fuel are threatening to join the opposition in voting against it or abstaining, which would be politically embarrassing for the prime minister.

Thatcher answered her critics with a vigorous defense of her policies at a London awards luncheon for small-business leaders yesterday. She pointed out that her government already had increased spending on nationalized industry, help for the unemployed and some social programs in response to pressure from business, the press and the dissenters in her Cabinet.

"Now what really gets me is this," she said, throwing away her prepared speech, "that it is very ironic that those who are most critical of the extra tax are those who were more vociferous in demanding the extra expenditures. What gets me even more is that, having demanded that extra expenditures, they are not prepared to face the consequences."

"I believe this government has taken the wise and moral course, and I will challenge anyone who takes the contrary view," she said. "So when people say that this is a no-hope budget, I can only say to them that this budget is the only hope for Britain's sustained and genuine revival."

But the vast majority of independent economic analysts in universities, think tanks and stock brokerage houses regularly consulted by the media have predicted that the budget would only deepen and lengthen the recession. They and other commentators also concluded that the budget and the ravages of recession made it almost impossible for Thatcher to realize her primary goals of significantly reducing government spending and taxation by the time of the next national election in 1983 or 1984.

In four rounds of painful budget-cutting so far, her government has succeed in curtailing spending on roads, transportation, housing, education and some social walfare programs, among other items. Thatcher also is gradually shrinking the bureaucracy through attrition and trying this year to hold down pay raises for government employes despite disruptive civil servants' strikes.

But because of the recession, spending has been increased for unemployment benefits and grants and loans to government-owned auto, mining, electronics and steel industries.

The government's plans to do better on trimming expenditures the next two years are imperiled by commitments already in the pipeline for nationalized industry and defense, plus the rising cost of still-increasing unemployment.

Political analysts and Thatcher, according to aides, see this year as a crucial political test. Unless the recession bottoms and out and she can offer sufficient help and hope for business, it is believed, she could face an ultimatum from her own Cabinet to change course or be replaced as party leader and prime minister in time for the Conservatives to offer a new image to the voters at the next election.