Britain and the United States have found "very little support" among the European allies for efforts to move or boycott next summer's Olympic Games in Moscow to protest the Soviet invasion of Afghanistan, according to government sources.

The reaction has ranged from French hostility and West German and Italian skepticism about interfering with the Moscow games to the preference of many smaller nations, including Denmark, Norway, the Netherlands and Ireland, to leave the matter in the hands of their national Olympic committees.

British Prime Minister Margaret Thatcher had sought "concerted action with our allies" to persuade the International Olympic Committee to move the games out of Moscow. She and her Cabinet do not believe they can force British athletes to boycott the Olympics unilaterally, although the British Olympic Committee decided today not to formally accept its invitation to the Moscow games until after conferring with government officials.

The lack of support for moving or boycotting the games provides another example of the deep division among the NATO allies over how they should respond to the Afghan crisis. Only Canada and Britain have been ready to join President Carter in taking such strong steps as refusing to participate in the Moscow Olympics or cutting off high-technology exports to the Soviet Union.

British has found itself increasingly isolated among the European allies after taking the lead in trying to sell Carter's retaliator measures. This has appeared to aggravate British differences with the rest of the European Community over Common Market policies and other issues.

As a result, Thatcher may not go as far as Carter after all in the steps she decides to take against the Soviet Union, despite her hard-line foreign policy and staunch public support for Carter. Decisions are expected to be made by Thatcher and her Cabinet this week and announced Monday during a special all-day parliamentary debate on the Afghan crisis.

At last week's meeting of the 15 NATO countries in Brussels, Britain's deputy foreign minister, Douglas Hurd, unsuccessfully supported the efforts of U.S. Deputy Secretary of State Warren Christopher to persuade the allies to join the U.S. embargo of high-technology trade to Moscow.

At the concurrent Brussels meeting of the nine Common Market nations, eight of whom also are members of NATO, the British representative, Sir Ian Gilmour, tried in vain to extend the Common Market's support for the U.S. embargo on grain exports to the Soviets to cover subsidized sales of surplus Common Market butter. France, Denmark and Ireland blocked his attempts to make permanent a temporary halt to the butter subsidies on sales to the Soviets.

Although Christopher claimed in Brussels that he had found "a strong and growing tide" of support for moving or boycotting the Moscow Olympics, Britain again offered the only strong support. Then, late last week, possibly to avoid being out alone on the limb in Europe on this issue, Thatcher announced that Britain could not act on the Olympics without support from many more nations.

She acknowledged that final Olympic decisions were in the hands of the International Olympic Committee and the various national Olympic committees, which have strongly opposed interference with the Moscow games.

Lord Killanin of Ireland, the president of the International Olympic Committee, said today he would discuss President Carter's opposition to the Moscow Olympics with his executive board next month, just before the Winter Olympics at Lake Placid, N.Y.

But throughout the weekend, he and other Olympic committee officials sharply criticized both Carter's boycott threat and Thatcher's campaign to move the games from Moscow.

[Meanwhile, reactions outside Europe to President Carter's decision to encourage moving or boycotting the Moscow games were lukewarm. The official New China News Agency, however, reported on the decisions by Saudi Arabia, Qatar and Djibouti not to take part in the games, fueling speculation that Peking was considering a boycott. China only recently regained a seat on the International Olympic Committee and the Lake Placid Winter Olympics will mark its return to Olympic competition after a long absence.]

The French government has been the most hostile among the allies to suggestions of moving or boycotting the Moscow Olympics, and has frequently repeated its intention to participate without reservations.

The West German government has taken no official position but is known to be skeptical about trying to pull out of the Moscow games. A government spokesman, however, recently said, "Should the American president and other government chiefs decide not to participate, then German solidarity will not be lacking in the discussions at NATO."

The Bonn government was embarrassed by reports that its NATO ambassador, Rolf Pauls, appeared to favor boycotting the Moscow Olympics at an emergency NATO meeting on New Year's Day. Pauls reportedly mentioned Hitler's 1936 Olympics in Munich and said a boycott then might have changed the course of history. While not denying that Pauls actually said this, the West German government later insisted that he had not suggested boycotting the Moscow games.