Responding to an urgent U.S. request, Britain is ready to join France and Italy in contributing troops to the multinational Sinai peacekeeping force called for under the Camp David agreements, according to European diplomatic sources.

The British decision is contingent, the sources said, on the 10 members of the European Community agreeing on a formula for tying participation in the Sinai force to progress toward a comprehensive Middle East peace settlement, including solution of the problem of Palestinian self-determination.

The favored approach appears to be the European Community's encouragement, without formal endorsement, of some form of the eight-point peace plan suggested earlier this year by Crown Prince Fahd of Saudi Arabia, according to several European diplomats. The sources said they expected a statement from the European Community countries within the next few days linking the plan with formal agreement by Britain, France and Italy to participate in the Sinai force.

The Reagan administration is pressing for a declaration of European participation in the Sinai force to carry the Camp David peace process through Israel's scheduled withdrawal from the last third of the Sinai on April 26.

French President Francois Mitterrand said yesterday in Williamsburg, Va., after talks with President Reagan, that France already has decided to participate in the Sinai force. European sources said Italy was likely to follow the French lead.

The British government, which currently holds the presidency of the European Community, believes that with the establishment of the Sinai force little more progress toward a Middle East settlement can be expected under the Camp David agreement and is seeking other ways to involve Israel and the rest of its Arab neighbors in negotiations on the Palestinian issue. Israel has resisted such negotiations until now.

Britain and the other European Community nations also want to avoid alienating Arab nations, particularly Saudi Arabia, by becoming part of the Camp David process through participation in the Sinai force, according to British sources. They said they fear that joining in the Camp David process could be seen as a withdrawal by the Europeans from the independent stand they have taken in calling on Israel to recognize the Palestinians' right to self-determination and on the Palestine Liberation Organization to recognize Israel's right to exist.

"Steps have to be taken to protect European independence on the Mideast," said one source here, who added that urgent consultations are continuing within the European Community.

A European diplomatic source said Britain did not want to play the leading role in agreeing to participation in the Sinai force, preferring to follow the lead of France and Italy with the backing of the other seven European Community countries.

British sources stressed today that "no formal decision" has yet been made by Britain and that the European Community foreign ministers decided at a meeting here last week to seek "a joint decision" by all 10 countries on the British, French and Italian response to the American request. But the sources here added that Britain and the rest of the European Community "will be influenced" by what France and Italy have made known about their intentions.

French Foreign Minister Claude Cheysson said in an interview published in Paris this week that with the completion of the Israeli withdrawal from the Sinai and what he characterized as European "contacts" with Egypt, apparently referring to participation in the Sinai peace force, "we will perhaps have a bridge between Camp David and the Fahd declaration" on which to build future peace efforts in the Middle East.

British sources pointed to previous European statements welcoming Fahd's proposals, and the decision last week by the European Community foreign ministers meeting here to send British Foreign Secretary Lord Carrington as their representative to Saudi Arabia in the next few weeks to discuss the Saudi plan.

Fahd called on Israel, under international guarantees or supervision, to withdraw from all Arab territory it has occupied since 1967, including East Jerusalem, and agree to establishment of a Palestinian state with Arab Jerusalem as its capital.

He also emphasized the right of states in the region to live in peace, which has been widely interpreted -- although not by the Israeli government -- as an offer of Arab acceptance of Israel's sovereignty within its pre-1967 borders.

Carrington will be seeking in Saudi Arabia "to identify common ground in Fahd's eight points and the Venice Declaration," in which the European Community stated its position on Palestinian self-determination and Israeli sovereignty, according to a senior European diplomat who attended last week's meeting here.

He said the 10 European Community nations -- Britain, France, Italy, West Germany, Denmark, Belgium, the Netherlands, Luxembourg, Ireland and Greece -- "are not moving to endorsement of the Fahd proposals as they stand, but want to encourage the Saudis."

The sources said a decision on the joint stand by the community is hoped for by the time the foreign ministers meet again next Tuesday in Luxembourg.

Cheysson said in the Paris interview that Fahd's declaration "gives a basis for negotiation that is fairly intelligent . . . even if we Europeans cannot accept all its elements."

Mitterrand indicated in Williamsburg that he saw the Fahd proposal as a positive step to be encouraged although it should not be seen as an answer to the problems of Palestinian self-determination, sovereignty over Jerusalem or Israel's territorial borders.

He also expressed skepticism about the European Community's emphasis on a role in future negotiations for the Palestine Liberation Organization, whose involvement Israel adamantly opposes. This approach had been agreed to by France under former president Valery Giscard d'Estaing.

British diplomats, according to informed sources, are disappointed that the Reagan administration has not pressed Israel to be more flexible in its approach to the Palestinian question. The sources also expressed skepticism about the administration's emphasis on efforts to enlist both Israel and Arab countries in efforts to defend the region from potential Soviet or Soviet-backed threats.

The sources said British diplomats still see Arab-Israeli relations and the Palestinian problem as a much greater threat to peace and stability in the Middle East than the perceived Soviet threat.