London — With the emigration of Lidiya Vashchenko, hope is growing here that the Kremlin may be ready to free the ''Siberian seven'' - Russian Christians who took refuge in the basement of the American Embassy in Moscow and have lived there for almost five years.
Lidiya Vashchenko - one of the seven - has accepted a KGB offer to let her emigrate. She has left Moscow and is expected to go to Israel via Vienna.
Danny Smith, campaign organizer of a British group called ''Free the Siberian Seven,'' says this raises the prospect of new action toward the other six. Speaking before Lidiya accepted the KGB offer and left the Soviet Union, Mr. Smith said the offer could be a signal that the Kremlin wants better ties with the US in general.
Some Soviet emigre sources here also believe the Kremlin is preparing to free dissident Anatoly Shcharansky, jailed in mid-1978 for 13 years on charges of espionage.
The emigres base their feelings on the fact that Soviet leader Yuri Andropov recently wrote to French Communist leaders assuring them that Mr. Shcharansky was well.
''No suah letter would have been contemplated unless something is being planned,'' says an emigre with long experience in KGB tactics.
The KGB offered March 23 to let Lidiya Vashchenko emigrate to Israel or West Germany - but not to the United States, which was her preferred destination. She had spent 31/2 years in the embassy before being taken out to a Moscow hospital in January 1982 after a long hunger strike. She was subsequently permitted to return to Chernogorsk, in Siberia, where she has lived with other family members.
The local KGB had beaten, followed, and harassed her in other ways, the family reported. Never had it encouraged her to think an emigration application would be accepted.
The story of the Siberian seven (actually the ''Siberian six'' since Lidiya left) is one of the most dramatic human sagas in US-Soviet relations in recent years. Lidiya, her sisters Lyuba and Lilia, their parents, Pyotr and Augus-tina, and Maria Chmykhalova and her son Timofei, rushed past Soviet guards outside the embassy in June 1978.
For 16 years they and other Siberian Pentecostalists (similar to some US Baptists) tried to escape Soviet religious persecution and find freedom to worship in the US.
They have refused to leave the embassy for fear of torture or death at the hands of the KGB. They want a guarantee that if they do leave, they can go to the airport and take a plane for the US. Lidiya left only because her health had deteriorated after the hunger strike.
So far Soviet officials have refused exit visas for the other six. In 1979 they offered to consider exit applications if the families returned to Siberia first, but the families did not believe the offer was sincere.
Although some in the embassy and in Washington have seen the seven as an irritant and a barrier to better US-Soviet ties, first the Carter administration and now President Reagan has allowed them to stay. The embassy has provided them with food and two clean, reasonably comfortable basement rooms.
Mr. Smith, who talks to the families in the embassy by phone once a week and has visited them in Moscow, is one of a number of Westerners who continue trying to free the two families. He is aided here by several members of Parliament. Several American diplomats who have served in the US Embassy in Moscow are active in the US.
Pyotr Vashchenko and his wife have vowed they will not leave the embassy until all 13 of their children are allowed to accompany them. Apparently they were happy for Lidi-ya to make up her own mind.
Lidiya's departure raises hopes that Moscow has decided to find a way to let the families go.
The Soviet dilemma is that 30,000 other Christians of the Vashchenkos' Pentecostalist faith want to emigrate. To let them go would, in KGB eyes, be to admit that Soviet citizens are unhappy in their workers' state. But if Israel or West Germany were the destination, Soviet officials apparently calculated that they could explain any departures to their own people by saying they are ''special cases.''
More than 200,000 Jews have been allowed out since 1970, but the rate has dropped dramatically since detente began to freeze over after the Soviet invasion of Afghanistan in December 1979. Numbers of Volga Germans have been allowed to go to Germany.
What might the new move mean for the six still in the embassy? ''We don't know yet,'' says Mr. Smith in London, ''but there is some reason to think that the Soviets may be under pressure to find a solution before the World Council of Churches meetings in Vancouver in July.''
The church council, which holds such meetings every seven years, is still arguing over whether religious freedom should be on the official agenda.