British Foreign Secretary David Owen, who flies to Washington this weekend for talks with Secretary of State Cyrus Vance on the many-sided Rhodesian deadlock, is described by aides as increasingly discouraged over prospects for a peaceful settlement.

Owen, however, is unwilling to give up as long as he thinks any chance for accord exists, the aides say.

His position was weakened last week when the Cabinet opposed any British contribution to a peace-keeping force for Rhodesia. Owen had not contemplated sending many troops to Rhodesia, but he had hoped to supply British officers for a multi-racial Commonwealth contingent to keep order during a transition period until a new, black majority government comes into power.

The so-called third force is only one of the many problems in Rhodesia over which Owen and Vance are expected to wrestle. The biggest, according to diplomats here, is the same one that has plagued the search for a peaceful solution since Prime Minister lan Smith gave a heavily qualified endorsement of majority rule last Sept. 24. That is who will be in charge of the guns - police and soliders - in the transition period until a new government is in place.

All sides - Smith and his white colleagues as well as four sharply divided black leaders - believe with some justification that whoever controls the guns will control the shape of the new state.

Owen and the United States had hoped to slice through this problem by putting control in the hands of a Commonwealth force. They are discovering, however, that no Commonwealth country is eager to get into the Rhodesian imbroglio.

The British are relunctant to be drawn in, no matter how lightly. The Nigerians are unhappy at the thought of possibly having to shoot unruly Rhodesian black guerrillas. The Indians are uneasy over any involvement.

The Rhodesians on both sides are equally hostile. Smith and the whites do not want it. Joshua Nkomo and Robert Mugabe, nominal leaders of the black guerrilla force, appear unalterably opposed.

It is possible that Bishop Abel Muzorewa, a moderate black leader, might like it. Judging from the crowds he draws in Rhodesia, he is the single most popular black leader and probably could win an open election. Precisely because of that, Nkomo and Mugabe do not want an election and simply demand that power be handed to them and their guns. The fourth black leader, Ndabaningi Sithole, appears to have neither guns nor popularlity.

U.S. Ambassador to the United Nations Andrew Young said Monday in London that the United States and Britain will press ahead with their effort to achieve a peaceful transition to black majority rule in Rhodesia despite a lack of success thus far. UPI reported. "The U.S. government is not disappointed with results so far," Young told reporters after a two-hour meeting with Owen. "We are a nation of optimists."

["No one is adopting any entrenched positions or concrete plans," Young said. "What we are after is an agreement between the majority of the people, both black and white, who are going to have to live together in peace in an independent Zimbabwe (Rhodesia)."]

Pro-Smith forces in Britain, notably in the Conservative Party, are calling for an "internal solution," one in which Smith makes a deal with Muzorewa and Sithole. Professional Diplomats are skeptical. Smith appears unlikely to accept Muzorewa's terms for one thing. For another, any deal that excludes the black guerrillas is not much of a peaceful settlement.

In Washington, Owen is expected to seek Vance's views on whether the white position is deteriorating, no matter how inefficiently and clumsily the black guerrillas have fought. The two foreign ministers will also plan to discuss whether there is any useful service still to be performed by John Graham of Britain and Stephen Lowe of the Graham of Britain and Stephen Lowe of the United States who have been quietly sounding out the various Rhodesian factions.

Finally, Owen and Vance will discuss whether new approaches should be made to the five neighboring African presidents and to South Africa. One of those five, Tanzanian President Julius Nyerre, has scheduled a state visit to Washington in early August, at which the Rhodesian question is likely to be discussed.

The five black states are thought to have influence over the Nkomo-Mugabe guerrilla force. South Africa could choke Rhodesia overnight by cutting its links to the outside world.

Less involved observers think that Anglo-American diplomacy is all but irrelevant now that no fresh ideas or initiatives are likely. Their expectation is that the struggle between whites and blacks in Rhodesia will be settled on the ground, by the fighting forces.