One of the Soviet Union's leading pianists, Andrei Gavrilov, has been allowed to stay in the West with his wife for one year, well-informed sources said today.

The decision followed reports from London that the 29-year-old Gavrilov and his wife Natalia had sought permission to stay in Britain.

Natalia is the daughter of Vladimir Alkhimov, a member of the Central Committee of the Soviet Communist Party and president of the Soviet State Bank.

According to the sources, Gavrilov asked Soviet authorities in London to extend his visa for one year so he could have a chance to travel and play with major world orchestras.

They said the decision to grant this request was made by top officials, including the new Soviet leader, Mikhail Gorbachev.

The couple arrived in England on Feb. 18 for a concert tour by Gavrilov, the 1974 Tchaikovsky Prize winner who is widely known here for his interpretations of Rachmaninoff, Prokofiev and Scriabin. British government officials were quoted on March 5 as saying that the Gavrilovs wanted to remain in Britain.

It was not clear whether the decision reflected a new, more lenient Soviet approach toward performers who want to live in the West for extended periods or whether the move was designed to spare from embarrassment such a prominent figure here as the president of the State Bank.

The Soviet cultural world has suffered a series of blows recently because stringent travel restrictions have prompted a number of performers to defect.

Among those who defected in recent years were conductors Kirill Kondrashin in 1979 and Maxim Shostakovich, son of the composer, in 1981; the violinist Gidon Kremer in 1980; theater director Yuri Lyubimov and film director Andrei Tarkovsky last year.

In 1983, another Tchaikovsky-Prize laureate, the 22-year-old Viktoria Mullova, a violinist, defected during a tour of Finland when she took a taxi to cross into Sweden and then went to the United States.

Other defectors include ballet dancers Rudolf Nureyev and Mikhail Baryshnikov, pianist Vladimir Ashkenazy, violinists Mark Lubotsky and Lydia Mordkovich, conductors Rudolf Barshai, Yuri Aharonovich and others.

Mstislav Rostropovich, the cellist who is now music director of the National Symphony Orchestra, and his singer-wife Galina Vishnevskaya were forced to leave in 1974 largely because of their friendship with novelist Alexander Solzhenitsyn.

Gavrilov and Mikhail Pletnev are regarded as the country's two leading pianists. Gavrilov is a prote'ge' of Sviatoslav Richter, the eminent Soviet pianist, and has been a flamboyant figure on the Soviet scene.

Natalia is Gavrilov's fourth wife. He was previously married to a Japanese and a Yugoslav woman.

Natalia has two children from her previous marriage. The children are in Moscow staying with her parents.