The British government, in a major policy shift, tonight agreed to a Commonwealth plan to draft a new constitution for Zimbabwe-Rhodesia and carry out new elections to end the 15-year-old independence dispute.

The dramatic breakthrough means that the Conservative government of Prime Minister Margaret Thatcher has abandoned its tacit support for the controversial April election of Bishop Abel Muzorewa as prime minister of Zimbabwe-Rhodesia.

Muzorewa's government also had gained widespread support in the U.S. Senate, which attempted unsuccessfully to pressure President Carter to lift economic sanctions against Zimbabwe-Rhodesia. British sources said the United States will play no role in the new plan.

The agreement, which the Commonwealth approved in a late-night meeting, appears to doom Muzorewa's hopes that his government would gain international recognition and a lifting of the sanctions.

Longtime observers of the Rhodesia issue, which has plagued Western relations with Africa since 1965, cautioned, however, that there were still considerable obstacles to a settlement.

There are three parties outside the Commonwealth, an organization of Britain and its former colonies, that would still have to accept the nine-point proposal. They are Muzorewa and his supporters among the 250,000 whites in Zimbabwe-Rhodesia and the two guerrilla leaders opposing the prime minister, Joshua Nkomo and Robert Mugabe.

In addition, there are substantive problems of arranging a cease-fire, disposition of the Rhodesian and guerrilla forces and the transition of power - if that stage is reached.

Nevertheless, there was an upbeat mood evident during the day as reports of the agreement leaked out. Several African and Western diplomats agreed that the plan - which also provides for a cease-fire and an end to sanctions - represents the best chance yet to resolve the seemingly intractable issue.

The nine-point plan was drawn up after a weekend of informal meetings by the leaders of six Commonwealth nations - Britain, Tanzania, Zambia, Nigeria, Australia and Jamaica - and Commonwealth Secretary General Shridath Ramphal.

The key points of the agreement call for Britain to draft a constitution "to grant legal independence...on the basis of majority rule" and "acknowledged that the government formed...must be chosen through free and fair elections properly supervised under British government authority, and with Commonwealth observers."

It also criticized the Muzorewa constitution as "defective in certain important aspects" and added that the new charter should include "appropriate safeguards for minorities."

The document welcomed a British indication that it would be appropriate for London to convene an all-party conference to achieve a new constitution and called a cease-fire and end of sanctions major objectives in bringing about a lasting settlement.

Thatcher criticized the current constitution for the first time in her speech to the Commonwealth Friday, but until tonight's agreement had refrained from specific proposals for a conference to draw up a new constitution.

More important, Thatcher had refused until today to deal with African demands for a new election. Those Africans maintained the April vote carried out by the white minority government of former prime minister Ian Smith was irrelevant and a fraud.

The election had won widespread support in conservative circles in both the United States and Britain as being "free and fair," thus warranting recognition of the Muzorewa government. Thatcher had seemed to be moving in this direction until last month and had said her government wanted to treat Muzorewa's government as "friends."

Despite indications of change in policy in her Friday speech, sources close to the prime minister have steadfastly refused to admit that any shift was occurring. Instead they have preferred to call each successive change "a progressive revelation of policy."

The reason for the British reticence can be found in Fleet Street press coverage of the conference, the first held in Africa.

Today's conservative Daily Telegraph ran a front-page headline: "Carrington and Foreign Office Overrule Mrs. Thatcher."

It has been known for weeks that Lord Carrington, the foreign secretary, and his senior staff opposed what apparently was Thatcher's original instinct: to recognize Muzorewa and ride out the consequences.

In a comment late tonight, Thatcher called the agreement "good news" for all parties to the conflict. "There would be no point in recognizing Rhodesia if the war went on," she said. Muzorewa's inability to end the guerrilla war has been one of his major problems.

The first major sign of change in policy occurred July 10, when Carrington reported to Parliament on British consultations with African nations. At that time he promised that the government would announce new proposals on Zimbabwe-Rhodesia after completing consultations at the Commonwealth conference.

Still, a major clash between Thatcher and the African members of the Commonwealth had been expected when the conference opened. She # received a hostile reception from the Zambian press, which labeled her a "racist."

Then on the eve of the conference, Nigeria, which had threatened Britain with economic retaliation if it recognized Muzorewa, nationalized the $150 million British Petroleum interest in a joint oil venture.

Carrington attacked the Nigerian move in a face-to-face confrontation with the Nigerian foreign minister, Maj. Gen. H. E. O. Adefope, at a reception on the lawn of the National Assembly, saying Britain would not be bullied.

Nigeria did some tough talking at the opening of the conference, implying it would pull out of the Commonwealth unless Britain came up with specific proposals. The British had come to the conference saying this would be the culmination of consultations, and hard proposals would be made only after Thatcher returned to London.

Thatcher has scheduled a Cabinet meeting for Friday, one day after her return to London, and could announce more details of her proposals soon after, depending upon the reception she gets from her party's right wing.

For most of the day British delegation refused to comment on escalating reports that the eight-member Commonwealth group had reached agreement on a plan. Persistent leaks about the contents of the agreement came from the Australian delegation. Australian Prime Minister Malcolm Fraser has sought to bridge the gap between Britain and Africa on the Rhodesia issue.

While still refusing to confirm or deny the reports during the day, British sources did little to hide their irritation over the leaks. Asked about reports that the Cabinet would meet Friday, one source said: "If Mr. Fraser says we will meet on Friday, I guess we must not disappoint him." CAPTION: Picture 1, MARGARET THATCHER...abandons support of Muzorewa; Picture 2, BISHOP ABEL MUZOREWA...little hope of recognition