Prime Minister Margaret Thatcher said today that convicted spy Geoffrey Arthur Prime apparently acted alone in passing secrets to the Soviets, but any possibility that he knew of other espionage agents in the British government would be "exhaustively investigated."

In a statement to Parliament, Thatcher said, "Investigations so far have yielded no evidence which contradicts Prime's own statement that no others were involved in his activities."

But, she said, now that he had pleaded guilty to spying for the Soviets during a period of 15 years, authorities would probe for answers to three major questions: how he managed to escape detection for so long, how much damaging information he had given the Soviets, and whether he knew of anyone else "in the public service" involved in espionage.

Prime was sentenced yesterday to 35 years in prison for espionage and a further three years on the morals charges that eventually led to his arrest for spying. First in the Royal Air Force and then for nine years as a Russian-language specialist with British intelligence, Prime delivered secrets to the Soviets that prosecutors said did "exceptionally grave damage" to Britain and its allies.

In the first official account of what material Prime gave the Soviets, Thatcher said he passed "information which must have alerted them to the state of our knowledge of certain important aspects of Russian defense arrangements, and to the ways in which that knowledge was obtained." This refers to Prime's work with Soviet communications intercepted by Britain.

Thatcher said there is no evidence that Prime had "access to any classified information about British or allied military dispositions or intentions, or to any information which could have endangered the lives of agents." The Washington Post quoted American intelligence sources as saying such material was involved.

The prime minister's remarks were an attempt to deal with the most serious allegations of security lapses that remain in the aftermath of Prime's conviction. The London Times today reported that U.S. intelligence sources believe that as many as "three other agents" have penetrated Government Communications Headquarters, the British intelligence agency where Prime worked.

Moreover, a number of members of Parliament have called for a reexamination of the procedures for granting security clearances in light of the fact that Prime underwent four such checks without being detected as a spy.

In referring the case to the government's special commission on security, Thatcher said that "now that the trial proceedings are complete, all these questions must be further and exhaustively investigated." Prime, his defense lawyer said yesterday, had agreed to cooperate in such a probe.