How many US, British secrets have leaked to Soviets?

A new flurry of spy cases and allegations here raises anew the question of just how many postwar United States and NATO secrets have been leaked to the Kremlin through undercover British agents.

Far too many, many British officials both in and out of Parliament have concluded - and now the air in London is thick with new reports and court cases that cast new doubt on British security practices.

It is all deeply worrying for the Thatcher government, which prides itself on being a loyal ally of the US.

Prime Minister Margaret Thatcher is under strong pressure now to launch yet another investigation of U.K. security precautions, including the ''positive vetting'' clearances, which failed at least twice to uncover Geoffrey Prime, who spied for the Soviet Union for 14 years.

Lord Chief Justice Lane, sentencing Mr. Prime recently to 35 years in jail for sustained spying at the Allied intelligence listening post at Cheltenham, said the former intelligence translator had done ''incalculable harm.''

The Cheltenham center shares intelligence intercepts with the US. Prime could have told the Soviets what frequencies were monitored, thus encouraging disinformation and signaling what codes had been broken.

US Defense Secretary Caspar W. Weinberger admitted Prime's acts had created a ''serious breach'' but added that they had not been ''catastrophic.''

Now a new case of alleged attempted espionage has emerged from the British Army Intelligence Corps in Aldershot, the group that monitors foreign armed services' strengths, weapons, tactics, and techniques.

At the same time, two Cheltenham employees have died under circumstances that aroused suspicions in and out of Parliament. And a British diplomatic secretary, Rhona Ritchie, was convicted Nov. 29 of leaking intelligence secrets to an Egyptian with whom she had an affair while serving at the British Embassy in Tel Aviv.

In an unrelated case, a Canadian professor, Hugh Hamilton, is charged with leaking secrets while working with NATO in Paris between 1956 and 1961.

Confronted with all this so soon after the sensational Prime case, and mindful of a string of security breaches since World War II, even the right-wing Monday Club group of Conservative members of Parliament has joined the ranks of those pressing for a thorough new probe.

The Monday Club calls for a judicial inquiry, saying, ''The time for bland assurances is long past.'' Swansea MP Donald Anderson argues that Parliament itself should appoint a committee of inquiry.

On BBC radio Nov. 29 Mr. Anderson alleged that the White House is upset with Mrs. Thatcher for assuring it repeatedly that Prime had been little more than a clerk. Mr. Anderson also said Prime was one of a ring of agents at the post.

The US Embassy in London said later it had no information about the report. The embassy itself has not been commenting on security issues.

Mr. Anderson also called for the introduction of US-style lie-detector tests throughout British security services. At present, the services do not use them.

In the newest case, a so-far unnamed lance corporal with the Intelligence Corps at Aldershot is under investigation for conduct ''prejudicial to good discipline.'' The Ministry of Defense will confirm only that a man has been under investigation. The ministry will not comment on a report in the Sunday Telegraph newspaper Nov. 28, and later echoed in other newspapers, that he is suspected of trying to leak secrets to the Soviet Embassy in London.

Some officials here doubt that a man of such junior rank would have had access to really sensitive material, but the worrying aspect is the state of security clearances.