In a dramatic demonstration of growing opposition to Prime Minister Margaret Thatcher's harsh economic policies, a member of Parliament tonight quit the governing Conservative Party in the middle of a debate on its unpopular tax-raising budget.

Christopher Brocklebank-Fowler, a Conservative legislator since 1970, became the first Parliament member to quit the ruling party in 75 years by declaring in a crowded House of Commons that he is joining the new Social Democratic Party in the center of the British political spectrum.

He then walked down from government benches and crossed the dividing aisle to sit in the facing opposition benches with the 12 Social Democrats. They had only recently defected from Labor, the largest opposition group that has turned sharply to the left while Thatcher has moved the Conservatives to the right.

His defection reduces the number of Conservative members of Parliament to 336 against 255 Labor members, 13 Social Democrats, 11 Liberals and 16 others from various regional parties in Northern Ireland, Wales and Scotland. Thatcher's government still has a 41-seat majority overall and does not have to face an election before 1984. But Thatcher herself is believed vulnerable to a rebellion from within her party if her government is unable to show soon some improvement in the economy besides falling inflation.

More than two dozen Conservatives tonight joined the opposition in voting against or abstaining on the most unpopular tax increase, which adds about 50 cents to the price of a gallon of gasoline. Although the measure still passed by 14 votes, so many defections from Britain's strict party discipline for key economic policy votes constituted a political embarrassment for Thatcher and another measure of the discontent in her party.

Still more Conservatives complained in tonight's parliamentary debate about the dampening effect on the depressed British economy of stiff tax increases in the Thatcher government's latest budget. Criticizing Thatcher's single-minded fight against inflation, Norman St. John-Stevas, fired by Thatcher earlier this year as leader of the House of Commons, said it is "not sensible morally to say that we should pursue one economic aim to exclusion of all human and social values."

No other Conservative member of Parliament is expected to follow Brocklebank-Fowler any time soon. His move nevertheless gave a big symbolic boost to the fledgling Social Democratic Party. According to public opinion polls, it is equally attractive to Labor and Conservative voters as an alternative, in alliance with the Liberal Party, to Labor's more militant socialism and Thatcher's free market orientation.

Brocklebank-Fowler's strong criticism of Thatcher's government for failing to carry out its promises to cut taxes and spending on government bureaucracy and create a better climate for business are shared by a sizable minority of Conservative members of Parliament, including a number of Thatcher's Cabinet. Some have publicly expressed their dissent, while others have privately made it clear to fellow politicians and reporters.

But they have indicated they will stay in the government and try to change its policies. Many are pressing for action by Thatcher before the end of the year to ease the squeeze on private industry during Britain's worst recession in a half century. They want further reductions in interest rates and taxes on business, some form of relief from high energy costs and innovative forms of government and private investment in capital improvements such as roads, railroads, sewers and telecommunications that would create new business and jobs.

Thatcher has so far responded by attacking her critics as lacking the "guts" or "morality" to continue supporting her policies for reducing inflation and government borrowing. Higher taxes were temporarily necessary, she has made clear, because dissenters in her Cabinet made it impossible to cut government spending as much as she sought.

"This government," Brocklebank-Fowler said today, "has knocked the stuffing out of British industry" and "created conditions which have caused record levels of bankruptcies and put hundreds of people [out of work]. The prospect of securing employment for the majority to those now unemployed is very remote unless there is a change in the government's policies."

To loud cheers from opposition benches, he said he greatly regrets that "members of the present Cabinet who disagree profoundly as I do with the government's policies are not showing a similar degree of courage" and joining him in resigning.

Arguing that Britain faces "massive unemployment and social disintegration" because of "mismanagement" of its economy by both major parties in recent years, he said the country "wants and deserves a new deal" from the Social Democratic Party.

"There are a good many Conservatives who feel as I do," Brocklebank-Fowler told reporters later. "Whether any of them will follow my course of action is entirely up to them."