Britain's Trade Ministry took formal steps today to prepare a challenge to the U.S. restrictions on sales of equipment for the Siberia-Western Europe pipeline.

The ministry issued an order under the Protection of Trading Interests Act of 1980, asserting that the U.S. move was damaging to British trading interests. This enables Britain to take whatever legal steps are available to overturn the embargo.

The ministry said such measures might be taken if all other efforts at persuasion were to fail.

British officials also said today that the government believes an unnecessary crisis over economic issues has erupted between the United States and Europe, and is urging the United States to reassess decisions that could have serious political consequences on the Western alliance.

Prime Minister Margaret Thatcher shares the unhappiness of other European leaders over the Reagan administration's decision to extend restrictions on equipment for a Soviet natural gas pipeline and impose additional tariffs on steel imported from European Community countries. But Thatcher, unlike many of the others, believes she can still prevail on Reagan to revise the policies and hopes to play a mediating role, sources said.

The prime minister, they said, believes, a "crisis of European confidence" in the United States has developed since last month's economic summit at Versailles and the subsequent announcement of American trade restrictions. They added that Washington would make a serious mistake in underestimating the scale of the difficulties merely because similar problems with Europe--especially over dealings with the Soviets--have emerged before.

This British view was instrumental in toning down an angry denunciation of the United States sponsored mainly by the French at the meeting of community leaders that ended in Brussels yesterday. Thatcher told the others that such a "declaration of economic war" would be counterproductive, her aides said. The final version expressed concern over U.S. moves, but stopped short of vilification.

Britain's determination to play a role in resolving the latest flareup in alliance ties seems to reflect Thatcher's enhanced self-confidence following British successes in the Falkland Islands war with Argentina.

"She has shown her commitment to principle," one official said, "which should give her credibility in explaining the European dilemma to someone like Ronald Reagan."

Thatcher raised the pipeline issue with Reagan when she met him in Washingon last week. A British firm, John Brown Ltd., has a contract worth almost $200 million to make turbines, in part using equipment made by a General Electric subsidiary. Under the U.S. sanctions, the British company would be unable to fulfill the contract.

Thatcher's position, and that of other Europeans, is that sanctions should not be extended to existing pipeline contracts because of the potentially serious damage on companies holding the contracts. Moreover, many of these companies are arguably beyond the reach of U.S. regulations, but were affected nonetheless because of restrictions on the use of American technology.

On steel, the proposed U.S. tariffs on community imports would deal a severe blow to a British steel industry already in severe recession. Britain's trade minister, Peter Rees, is in Washington to make the case again that steel curbs, in addition to the pipeline equipment embargo, could lead to retaliatory action by the Europeans against American goods.

But the burden of Thatcher's arguments to the Reagan administration, as conveyed personally last week and repeatedly through British diplomatic channels, is, in the words of one official: "Punishment that you give the Soviets with the pipeline sanctions loses its purpose if it is so unacceptable to American allies."

British officials believe that as a result of Anglo-American cooperation during the Falklands crisis, a special rapport between Thatcher and Reagan was forged. Although the United States now would prefer to see Britain open negotiations on sovereignty of the islands with Argentina, officials here believe that a measure of "wartime" solidarity still exists between Washington and London.

As the British see it, the departure of Secretary of State Alexander M. Haig Jr. removes the staunchest advocate for the European position from the administration, but also should ease some of the controversy from the debates over issues such as the pipeline in Washington. Officials here hope Reagan can be persuaded that it is worth reversing all or part of the new pipeline restrictions to bolster the alliance and that Thatcher, who basically shares the president's hard-line view on the Soviets, can make the case best.

In reporting to Parliament on her talks with Reagan, Thatcher said she agreed with the president, on "the need for . . . progress" toward liberalization of the martial-law government in Poland, which the pipeline sanctions are intended to encourage, "while reiterating the reasons why we thought existing commercial contracts should be exempted."

At least part of Thatcher's leverage with the president is undermined by Britain's continued adherence to a community policy that, in effect, provides credits at below-market rates to British companies doing business with the Soviets. At Versailles, the United States pressed its allies to abolish such subsidies. British trade with the Soviets is relatively small, about 1.2 percent of the country's exports, or roughly the same amount as trade with Finland.