The Reagan administration and its senior European allies, in a week of top-level discusssions here, have begun the process of easing mutual apprehensions and rescuing a storm-tossed Atlantic alliance.

Three days of meetings with British Prime Minister Margaret Thatcher ended with an unexpected "extremely social" call on President Reagan yesterday morning. As Thatcher departed for New York and London, a U.S. spokesman said Anglo-American basic agreement had been reached "on all major strategic issues."

"It was difficult to pry them away from each other at the end," said White House press secretary James S. Brady of Reagan and Thatcher. Their chemistry is right. . . . They hit it off." Switching to another metaphor, Brady added that the two leaders "have stared down the same gun barrel."

On the substantive side a senior State Department official conceded that "differences of view and approach," some of them long-standing, remain after the week of meetings here with Thatcher, British Foreign Secretary Lord Carrington and French Foreign Minister Jean Francois-Poncet. But the official went on to emphasize the the new administration's aim is to reduce and manage disagreements through the consultation process which has now begun.

Two tenuously related circumstances, Moscow's unexpected proposal for a Soviet-American summit meeting and the U.S. drive to stop the flow of outside arms to the civil war in El Salvador, were central items in the talks, which ranged over nearly every region of the world. From all appearances and the testimony of participants, the process of mutual education and accommodation on these matters by Reagan and the European leaders was particularly important.

Soviet President Leonid Brezhnev's summit proposal last Monday was seen by a senior British statesman as both an attempt to show genuine interest in the relaxation of tensions and a tactical maneuver to escape responsibility for greater East-West tension, thus bidding to divide the West if the olive branch were ignored.

The U.S. decision, as explained to the allies, was not to refuse summit dialogue with the Soviets, nor to rush to such a meeting. Instead a series of statements at the White House and State Department laid down requirements intended to be firm enough to stave off an immediate meeting but flexibile enough to permit the administration to proceed to such a session whenever this seems desirable.

As summarized at the State Department Wednesda;y, the U.S. position is that a summit meeting with the Russians "should have a clear purpose, be carefully prepared, and there should be reason to believe that there would be concrete achievements." Less precise statements from Reagan and Secretary of State Alexander M. Haig Jr. also suggested that Soviet activity worldwide would bear on the U.S. summit position.

Senior European diplomats expressed satisfaction with these conditions, which leave Moscow to prove that a summit meeting is warranted yet do not provide much fodder for allegations that Washington is refusing to meet. France's Francois-Poncet, for example, left his final meeting with top American officials describing the U.S. positions on East-West dialogue as "well-balanced."

Another major portion of the discussions dealt with El Salvador, which the Europeans consider well within Washington's special sphere of influence as a problem in the American "back yard." According to sources on both sides, the Europeans were not requested to do anything concrete, but were asked to be indirectly helpful by not raising obstacles.

The Europeans' main concern was the overwhelming emphasis here on the military side of the Salvador issue, and the relative de-emphasis on the social, economic and political woes at the root of the civil strife in that country. This concern arose from two sources: the political clout of important socialist parties and other elements of the public back home in Europe which find the Salvadoran rightists repugnant, and a more general worry that a military-minded Washington might tend to ignore local political realities, which the Europeans consider crucial in nearly every Third World problem, in the preoccupation with East-West conflict.

Participants in the White House meetings found Reagan more knowledgable and understanding than expected about the local realities of Third World problems. Though there has yet been no change in Reagan's rhetoric about El Salvador, Haig went out of his way on Friday to speak of the need for "progress toward pluralization" in that country as well as "the achievement and preservation of human rights" and "the rejection of excesses aby the right as well as the left."

Even while being sympathetic and supportive of U.S. concern about the guerrilla war in its back yard, some of the Europeans were puzzled prior to their discussions here about the great emphasis and high priority placed on the tiny Central American country. "Now I understand it," said a French diplomat after exposure to the high ranks of the new administration. In his view, El Salvador is "the first manifestation of a general policy" of confrontation with Soviet-Cuban activities. "It is a signal" to the Russians, and thus important beyond the tangible facts, he said.

Among many others, the exchange of views with the European leaders covered the following points:

New ways to bring to bear greater joint military resources in the Persian Gulf, which provides 60 percent of Western Europe's oil (but only 15 percent of U.S. petroleum consumption). Thatcher told British reporters before leaving here yesterday that she had discussed a British contribution to a "multilateral rapid deployment force" for the area. U.S. officials believe she was referring to a "mini-RDF" intended to give Britain at least the beginnings of the new role in the gulf, once its virtual protectorate.

Arms control negotiations with the Soviet Union. Carrington reminded the Americans that these are part of the basis of public support in Europe for expanded defense efforts, and an explicit part of the deal by which European countries agreed to the placement of new medium-range missiles on their soil. In response, Reagan eased European concern for the moment by publicly reaffirming the arms control component of the Euro-missiles bargain. But there could be trouble later, administration officials conceded, if Washington delays too long.

The Middle East initiative launched under the aegis of the European Economic Community to display, largely for Arab comsumption, Europe's interest in an Arab-Israeli peace. The Reagan administration and the European leaders are reported to have had a thorough airing of respective viewpoints on this activity, which is repugnant to Israel and was cold-shouldered by the Carter administration. The Europeans are going ahead with their bid, but at a pace that is not likely to bring it to fruition before this summer, and U.S. officials expressed the expectation that it will proceed with greater sensitivity for Washington's viewpoint.

As the Atlantic alliance struggles to adjust to new circumstances and a new administration in Washington, the underlying erosion of confidence is of even greater importance and concern than outstanding difficulties on any paraticular set of issues, according to Reagan administration strategists. a

These officials expressed the belief, therefore, that the cooperative spirit of the top-level consultations here last week was as important as anything specific that was said. Washington officials were encouraged, they said, at the seeming eagerness of the British and French to educate Reagan and his senior team in the imperatives and realities as seen from Europe. And top European diplomats said they were impressed by the Reagan administration's willingness to listen at a moment when so many of its international policies are still in the formative stages.