Following the latest and most conspicuous failure of British and American diplomats to end Rhodesia's bloody conflict, they decided to lie low and abstain from fresh initiatives for awhile.

This, it was learned yesterday, was the central outcome of a private meeting here last Saturday involving Foreign Minister David Owen; Richard Mosse, the U.S. assistant secretary of state for African affairs; Anthony Lake, director of the State Department policy planning unit, and other key British and American diplomats.

Authoritative sources disclosed that the meeting, scheduled to last 90 minutes and actually consuming over three hours, was largely devoted to a cheerless review of the Rhodesian conflict. At the end, they agreed that neither Washington nor London could do much that was useful now.

The unsuccessful initiative was last month's secret meeting between Rhodesian Prime Minister Ian Smith and Joshua Nkomo, one of the two guerrilla leaders whose forces are closing in on the whites. Authorities here acknowledge that this meeting was designed by Owen, who had hoped to unblock the political stalemate in Rhodesia. U.S. officials are said to have greeted Owen's planskeptically but abstained from exercising a veto.

Diplomats strenuously deny that the meeting was designed to reach a settlement behind the back of Robert Mugabe, Nkomo's guerrilla partner. Instead, the U.S. and British officials had hoped that the Smith-Nkomo talks would lead to a conference of all forces, black and white, inside and outside Rhodesia.

As it turned out, the secret meeting was largely a disaster. It has infuriated Mugabe, who learned of it only after the talks took place, and then from Nigerian sources who had helped promote the meeting. This is seen here as an effort by Nigeria to keep a foot in both the Nkomo and Mugabe camps.

The Smith-Nkomo talks also split the fragile unity among the black African presidents who rule lands bordering Rhodesia.

President Julius Nyerere of Tanzania, a major supporter of Mugabe, is reliably reported to have spoken harshly to President Kenneth Kaunda of Zambia, the chief source of comfort for Nkomo.

The whole affair was capped by the downing of a Rhodesian civil airliner last week and the killing of 10 white survivors. Nkomo has said his forces brought the plane down but he denied that his men had killed the survivors.

Nkomo has now said that the proposed Anglo-American conference of all parties is "dead," although Mugabe promptly retorted that it is very much alive.

At the same time, the slaying of the crash survivors has made it impossible for Smith to make further moves toward the guerrillas, the diplomats here agreed. They see Smith's own position endangered by two right-wing white forces in Rhodesia. One is demanding air and ground strikes wherever guerrillas are thought to camp. The other wants to displace Smith and somehow negotiate a continued white-supremacist rule.

It is against this tangled background that Owen and the Americans decided last weekend to adopt a lower profile. John Graham of the British Foreign Office and Stephen Low, the U.S. ambassador in Zambia, have been traveling between capitals and rilla leaders trying to coax all sides to come together around a table. The two negotiators present at Saturday's London talks, have been instructed to sit back quietly now.

Despite the obvious failure of the Smith-Nkomo meeting, some Anglo-American diplomats argue that it has induced a new sense of realism about Rhodesia, making it evident that Smith's current power-sharing arrangement with unarmed black leaders inside the country no longer has currency.

That arrangement's principal black beneficiary, Biship Abel Muzorewa, once touted as the most popular black politician in Rhodesia, is now regarded as a lonely figure. His lieutenants, it is said, are deserting him in droves, anxious to be on a winning black side and convinced it is not Muzorewa's. Much the same thing, the diplomats concluded, is happening in the camp of the other principal signer of Smith's "internal settlement," the Rev. Ndabaningi Sithole.

The internal settlement was intended to pass nominal majority rule to blacks led by Muzorewas and Sithole but retain control of armed power in white hands. In contrast, the year-old Anglo-American plan would give much of the control of Rhodesia's armed forces to guerrillas led by Nkomo-Mugabe in the crucial period before any election was held.

Although London and Washington have agreed to hold still for awhile, the diplomats here recognized that they still exercise considerable influence on Rhodesian events. In response to a plea from Kaunda, who feared Smith would bomb an strafe his settlements in reprisal for downing the airline, the Anglo-American team urged Smith to make a measured response. The fact that London and Washington could send this message with the blessing of Smith's South African allies is thought to have been decisive.

In the event, Smith, who had promised stern measures, called only for partial martial law. This was regarded by Rhodesian whites as a "damp squib." It further undermined Smith's position among whites but prevented, for the moment, further inflammation of the struggle.

Owen, Moose, Lake and others meeting here were also conscious of domestic political pressures in Britain and the United States, where elections will be held soon. In both countries, these pressures are far stronger from the right than the left, the diplomats believe, far stronger on the side of Smith and the whites than on the side of the divided black guerrillas. Those pressures, in turn, are seen by the diplomats as a further reason for restraint now.

Some of the more independent officials present at the weekend gathering here would welcome more frankness over Rhodesia.

They say Britons and Americans should be told that Smith is finished, that the original plan to hold elections before a black independent state is declared has been overtaken by events. In their view, however, only a free-wheeling figure like Andrew Young, U.S. ambassador to the United Nations, could now say that black independence must come before - not after - an election.

The gloomiest diplomats, who have been most often right in the past, are now convinced that Smith and the whites will be driven from power, even by divided black guerrillas. They then expect that the Mugabe and Nkomo forces will battle each other for power.

In this view, Western interests lie in containing the civil war to Rhodesians or Zimbabweans, as they will then be called.These diplomats hope that the struggle will not widen to embrace Cuban and South African troops.

On which side Havana and Pretoria would fight is far from clear. Nkomo, regarded as more moderate, gets his arms from the Soviets, as do the Cubans. Mugabe, seen as the more militant ideologue, is aided chiefly by China, Moscow's resolute opponent. How South Africa would choose a favorite here is not easy to figure.

Above all, the pessimistic diplomats believe that London and Washington are steadily losing power to affect affairs in Rhodesia. These diplomats believed that both capitals are responding to rather than shaping the course of events. They even use language heard in equally stalemated Northern Ireland, where "the politics of the last astrocity" is usually paramount.