Britain said today that it will withdraw from membership in UNESCO on Dec. 31 for many of the same reasons stated by the United States last year in quitting the international agency, which both countries have said is biased against the West and spends too much money on bureaucracy.

To Parliament, Overseas Aid Minister Timothy Raison said the United Nations Educational, Scientific and Cultural Organization had "gone wrong" and was "harmfully politicized and badly managed."

Prime Minister Margaret Thatcher made the decision to withdraw despite urging from other European countries and from a broad spectrum of political leaders here, including members of her own Conservative Party, that Britain could accomplish more to change UNESCO by staying in.

Britain, along with the Reagan administration, has charged that UNESCO often involves itself in extraneous political issues, including taking stands and funding projects on nuclear issues, human rights and control of the international media that are addressed from the perspective of Eastern European members and detrimental to western values.

Raison said that up to 70 percent of the UNESCO budget was spent at its top-heavy Paris headquarters. He stressed overall support for the U.N. system and said Britain would maintain observer status, along with the United States.

But, he said, "we are determined that our support . . . should be for effective and efficient organizations. Unfortunately, UNESCO is not such a body."

Today's announcement fulfills notice given by Britain last year that it would leave unless substantial changes were made in organization and spending priorities. Although the government acknowledged that some steps had been taken, including budget reductions and depoliticized priorities agreed upon during UNESCO's general conference last month in Bulgaria, Raison said they were not enough.

In a statement, UNESCO said it "deeply regrets" Britain's move, which it said "must come as a surprise to all those who have been engaged over the past two years in a far-reaching effort to agree on UNESCO's programs, budget, structures and functioning."

Britain was due to contribute $9 million next year, about 8 percent of the organization's budget -- which was already cut by 25 percent, the portion of its budget formerly contributed by the United States.

The loss of what has been a prestigious British presence is seen as in some respects more damaging than the loss of funds. Britain has played a unique role in UNESCO since it was founded here four decades ago. Julian Huxley, its first director general, was one of many prominent Britons instrumental in developing and fostering the agency.

The government's decision, which Prime Minister Thatcher said was taken "in British interests," brought a storm of protest from a wide political spectrum, including many within Thatcher's Conservative Party. Raison denied charges that it had been made under U.S. pressure.

Opposition Labor Party spokesmen called the decision "shabby and disgraceful" and "a kick in the teeth for the Third World," whose nations form a majority among the 160 member states. Former foreign secretary David Owen, head of the Social Democratic Party, said it branded Britain an "international Philistine . . . , shown to be insular, inward-looking and mean-spirited."

A knowledgeable U.S. official said the Reagan administration had expressed its views to the Thatcher government, but denied that any pressure had been exerted. He said the administration and Thatcher "see eye to eye on a lot of the problems" of UNESCO. "Many of our criticisms are the same, and we're not surprised that they came to the same conclusion."

The official said, however, that the administration had begun to wonder in recent weeks whether Thatcher would be able to withstand opposition to withdrawal. Following hearings, an all-parties select foreign affairs committee of Parliament unanimously recommended continued membership.

Thatcher has received numerous appeals from abroad to stay in UNESCO, including those of the Commonwealth nations, the European Community, West German Chancellor Helmut Kohl and French President Francois Mitterrand.