London — If the new Soviet leader, Yuri Andropov, wants to signal warmer relations with the United States, he could do it dramatically and unmistakably by reopening two human-rights cases now back in the headlines.
This is the strong belief of human-rights activists in Britain, who are trying to generate new pressure and publicity on behalf of:
* Anatoly Shcharansky, one of the most prominent Soviet dissidents of recent years, now on a prolonged hunger strike in a Soviet prison cell.
* Two devout Christian families, known as the ''Siberian seven,'' who dashed into the US Embassy past KGB guards in mid-1977 and have refused to set foot outside ever since for fear of arrest and torture. The Vashchenkos and the Chmykhalovs want permission to emigrate to religious freedom in the US.
So far both cases help block any thawing of icy US-Soviet relations.
The Soviets have not responded to Western suggestions that they swap Shcharansky for Soviet spies in custody in the West. To the ''Siberian seven'' they have offered some concessions but no exit visas, and the families refuse to accept anything but emigration with all their children.
Now Shcharansky's wife, Avital, and other Jewish activists here, and a group campaigning to free the Siberian seven, are trying to use another event to help their cause.
This is an unusual 10-day visit to Britain by 11 Soviet church figures led by Russian Orthodox official Metropolitan Philaret from Kiev. The trip, which took two years to organize, is sponsored by the British Council of Churches and is to include two meetings with the Archbishop of Canterbury, Dr. Robert Runcie.
Quickly, both the Women's Campaign for Soviet Jewry, and Siberian seven campaigners Danny Smith and Joan Edgar organized a demonstration to be held outside St. Paul's Cathedral while a Soviet delegation is inside.
Meanwhile Mr. Shcharansky remains a symbol of US-Soviet friction over human rights. His case is the focus of sustained pressure by Jewish groups in the US, Israel, and elsewhere. Avital Shcharansky, who has not seen her husband for eight years, is in London seeking a meeting with Prime Minister Margaret Thatcher to mark Mr. Shcharansky's birthday Jan. 20.
Before she accepted her own exit visa from the USSR, Mrs. Shcharansky was promised that her husband would soon follow her. Instead, he was arrested early in 1977. In a blaze of world headlines in mid-1978 he received a jail sentence of 13 years on criminal charges arising from his efforts to emigrate.
His health has deteriorated. He has been kept in isolation and denied visits from his mother and brother.
In Washington, the State Department would like to see both the Shcharansky and Siberian seven cases solved quickly. So would the activists here, but the next move is up to Mr. Andropov.