Prime Minister Margaret Thatcher's predecessor as Conservative Party leader, Edward Heath, last night joined the growing criticism of her economic policies as unemployment continued to climb and industrial output fell further.

The latest financial plan of Thatcher's government -- a compromise of slightly lower government spending, higher taxes and a cautious reduction in interest rates announced in Parliament Monday -- has been strongly criticized from all sides in parliamentary debate and the British press.

Former prime minister Heath, who was replaced by Thatcher as party leader six years ago, directly challenged Thatcher's policies in Parliament for the first time last night, warning that they were destroying private business and risking unemployment on the scale of the depression of the 1930s.

"This problem of unemployment should be dealt with," Heath told Thatcher and her Conservative supporters in the House of Commons as opposition Labor Party members cheered him on. "Otherwise the risk to our party is very, very great and will defeat other purpose which we have in mind."

Heath said he found he was "not entirely alone in the Conservative Party" in his opposition to the harsh, doctrinaire monetarism of Thatcher's chief economic advisers. He said other Conservative members of Parliament supported his statement in a recent radio hookup with American economist Milton Friedman that Thatcher's policies, originally based on Friedman's monetarism, were "catastrophic" for Britain.

Heath urged Thatcher and her chancellor of the exchequer, Geoffrey Howe, to make their policies more flexible and begin steps to ease the recession and stimulate business.

He was joined in this plea by another former prime minister, James Callaghan, in his first parliamentary speech since retiring as Labor Party leader. Callaghan warned Thatcher that she risked social unrest in areas of high unemployment, and said "this is not the time to cut demand" with spending cuts and tax increases. Instead, he urged, "It is time when demand should be sensitively but properly increased."

Even some of Thatcher's staunchest supporters in the news media joined the attack. The tabloid Sun, which has the largest circulation in Britan, said Howe's latest economic plan "achieved the feat of offending the most people and doing the least good." Howe was depicted in a cartoon on the Sun's front page as a sadistic Nazi officer.

The Daily Mail newspaper and Economist news magazine however, both criticized Thatcher for not being radical enough in her efforts to shrink government and give private enterprise more economic freedom and incentive. The Economist warned Ronald Reagan, whom it endorsed during the U.S. presidental campaign, to study how "the British precedent" for his intended economic policies went wrong. "The Thatcher experiment," the Economist said, "is in trouble."

Thatcher acknowledged on BBC radio that her government has had difficulty cutting government spending, reducing its borrowing and controlling the money supply. But she insisted once again that the long-range prospects for her strategy were good.

"We shall in future see a real revival of our country's fortunes if we hold to the path we are now on," she said. "We are reaching the trough of the recession and it will start to turn up towards the end of next year."

But her government's current problems have revived speculation that Thatcher might be replaced as Conservative Party leader if her policies do not produce results or are altered substantially before the Conservatives next face the voters in 1983 or 1984.

Other observers expect Thatcher to make at least cosmetic changes in her Cabinet some time next year, possibly replacing the increasingly unpopular Howe as chancellor of the exchequer.