Britain announced today that it will send high-level emissaries to Rhodesia and its black African neighbors to lay the groundwork for eventual formal recognition of the black-majority government of Prime Minister-elect Abel Muzorewa.

Foreign Secretary Lord Carrington, outlining "the first significant steps" Britain's new conservative government will take to return Rhodesia "to legality in conditions of peace and of wide international recognition," said a senior Foreign Office diplomat will go to Rhodesia and "stay there for as long as possible to maintain and develop the closest possible contact with Bishop Muzorewa and his colleagues and to report to me."

The diplomat is to stay in Salisbury in Morimba House, the home of Britain's last envoy to Rhodesia.

Another emissary, most likely a senior Conservative politician, will travel to Africa to discuss the change in British policy with the British Commonwealth nations there, particularly the "front-line" black African states near Rhodesia.

When Prime Minister Margaret Thatcher was asked in the House of Commons whether this emissary also would meet with Robert Mugabe and Joshua Nkomo, the Rhodesian guerrilla leaders operating out of neighboring countries, she said, "I have no announcement or statement to make on that."

The two emissaries, who are to be named later will be seeking a way for Thatcher's government to restore Rhodesia, a breakaway colony, to legality and end British economic sanctions against it with a minimum of damage to British relations with the rest of Africa.

Both Thatcher and Carrington made clear again today the Conservatives' conclusion, based on a report from their own observers, that last month's election in Rhodesia was sufficiently free and fair to justify British recognition of Muzorewa's government in place of the white minority rule of outgoing Prime Minister Ian Smith.

"There has at last been an election in which every adult man and woman [in Rhodesia] has been enabled to cast a vote" and a black majority government has been elected, Carrington said in announcing the British government's plans to the House of Lords. "It would be morally wrong to brush aside an election in which 64 percent of the people cast their vote."

The ambassadors of the 35 Commonwealth nations - including Australia, Canada and former British colonies in Africa, Asia and the Caribbean - declared here last week that the Rhodesian election was a "gigantic fraud" and warned Britain against recognizing the Muzorewa government.

The Thatcher government has made it clear that no formal action will be taken before the possibly stormy August meeting of the Commonwealth heads of government in Lusaka, Zambia, which Thatcher and the queen will attend. Britain's economic sanctions agains Rhodesia come up for renewal in Parliament in November.

Today's announcement, two weeks after the Thatcher government took office here, is intended to buy time while assuaging pressure from the Conservatives'right wing for immediate recognition of Rhodesia. Muzorewa and Rhodesia's whites presumably will have an opportunity to try to make his government more acceptable to the rest of the world, possibly by reducing the disporportionate amount of power the whites retain in the civil service, courts and military, and to make peace overtures to the guerrillas. At the same time, Britain's emissary apparently will try to sell the new policy to the rest of Africa and the Commonwealth.

These plans reportedly were presented by Carrington yesterday to Secretary of State Cyrus Vance, who is holding discussions with Conservative government officials here this week on a wide range of issues. British sources said Vance was "supportive."

U.S. officials traveling with Vance said Vance felt that the Conservative government's plans were "the business of this government" and he did not foresee any U.S. objections to them.

President Carter must decide next month whether to change U.S. policy and lift economic sanctions against Rhodesia, as he was urged to do by an overwhelming vote of the Senate last week.

The Carter administration and the former Labor government here had previously insisted that only a prior settlement with the guerrillas and internationally supervised elections could solve the Rhodesia problem.

Although Vance and Carrington plan to talk more and Rhodesia, the rest of southern Africa and other topics Wednesday, no U.S. position on Rhodesia can be stated until Carter decides, U.S. sources here srington also announced today, after informing Vance yesterday, that another British representative, Foreign Under Secretary Richard Luce, would leave Wednesday for southern Africa to "learn at first hand about the remaining problems" in Namibia.

Carrington said Britain remains committed to the implemention of proposals by five Western powers - Britain, the United States, Canada, France and West Germany - for an all-parties settlement leading to U.N. supervised elections in Namibia.*