Britain's Conservative government today moved further along the road to recognizing Bishop Abel Muzorewa's black majority government in Rhodesia and lifting economic sanctions against that country.

In a detailed presentation of Prime Minister Margaret Thatcher's foreign policy to the House of Commons, Foreign Office minister of state Ian Gilmour said Britain will be "making permanent arrangments for continuing consultations with Bishops Muzorewa" through senior British officials staying in Salisbury "as often and for as long as may be necessary."

Through this new link with Salisbury, Thatcher's government would continue to pursue "our overriding objective," Gilmour said, "to return Rhodesia to legality and achieve the lifting of sanctions of peace and in a conext of wide international recognition."

Later today, Thatcher's government was strongly urged by fellow members of the Commonwealth of Nations not to recognize Muzorewa's government. The Commonwealth high commissioner, meeting here, declared as expected that last month's "internal settlement" election" in Rhodesia was "fraudulent" and Muzorewa's government therefore remains as illegal as the white minority government of Prime Minster Ian Smith that it is replacing.

Their action adds to the threat of serious conflict for Britain at the Commonwealth heads of government meeting this August in Lusaka, Zambia.

The Commonwealth, composed of former British possessions, has many members from Asia and Africa sympathetic to the cause of the Rhodesian rebels.

Gilmour said Britain would also "seek consultations with the African government principally concerned."

One option the Conservative government will be exploring is a prior settlement between Muzorewa and the black Patriotic Front rebels who boycotted the election. That had been the objective of the joint British-American policy toward Rhodesia before the Conservaties took office here.

Nevertheless Gilmour reciterated that this policy had been overtaken by "a fundamental change in circumstances inside Rhodesia" as a result of last month's election in the former British Colony.

He said that former colonia secretary Alan Lennox-Boyd, now Lord Boyd, who led a team of Conservative representatives observing the Rhodesian election, had reported favorably on it on Thatcher.

"Although he makes certain reservations, Lord Boyd's broad conclusion," Gilmour told the House of Commons, "is that the election in Rhodesia was fair, in the sense that the electoral machinery was fairly conducted, that it was as free as possible in the circumstances, and the result represented the wish of the majority of the electorate of the country."

Emphasizing that the Thatcher government intends to move with caution, Gilmour said, "We shall recognize the present realities of the situation in Rhodesia, but we shall not lose sight of the wider international considerations. International support and recognition, and cooperation with other African states, must be vital to a landlocked state in central Africa, above all one which is still engaged in a cruel civil war.

"We are bound to consider whether any way can be found, even at this stage, to heal the divisions and bring an end to the war. We must take due account of the need for consultation with the countries whose friendship Rhodesia will need . . . if it is to prosper."

Former Foreign Minister David Owen, one of the architects of the joint-U.S. Rhodesia policy, responded by warning that recognition of the Muzorewa government would be 'a grave error." He said Britain "could be rightly accused of breaking faith by every Commonwealth government, including Canada and Australia."