Britain's top security officials are trying to solve the mysterious death of a Bulgarian defector who said he had been poisoned by an umbrella tip.

Earlier this year the defector, Georgi Markov, once one of Bulgaria's most prominent playwrights, completed a series of 14 broadcasts for Radio Free Europe recounting his personal relationship with Todor Zhivkov, Bulgaria's president and leader of its Communist Party.

An autopsy on Markov, 49, failed to determine yesterday whether or not his death on Monday was natural. Police sources said that modern poison agents are so sophisticated that acience may never be able to ascertain how Markov died.

Before he died, Markov himself was in no doubt about what had happened. From his hospital bed, he told friends he was the victim of a man with a foreign accent who stabbed him in the leg with an umbrella last week.

Knowledgeable intelligence sources here are uncertain whether Markov, a broadcaster for Western stations to the East, was in fact the prey of Communist agents. One source said he had a "gut feeling" that "a job" had been done on the dead man. But this same source pointed out that the Soviet KGB kills defectors it wants to eliminate in a matter of months, and Markov came to Britain in 1970.

Scotland Yard's failure to answer conclusively how Markov died comes as no surprise to intelligence veterans here. Traditional poisons like cyanide or prussic acid display tell-tale symptoms in the blood. But professionals no longer use such straightforward agents and now kill with highly concentrated dose of relatively innocent-appearing substances like nicotine.

There is little doubt that Markov and his broadcasts were a nuisance to the East Bloc. Like other emigres, he lived in fear of his life. For seven years, he has been broadcasting segments of his unpublished memoirs, identifying allegedly corrupt Bulgarian leaders, over Radio Free Europe and Deutsche Welle.

The former is a U.S.-government run station in Munich formerly controlled by the CIA. The latter is a West German government station. Both are beamed to Eastern Europe.

[A spokesman at Radio Free Europe said Markov had worked as one of several hundred free-lance broadcasters for the radio. Between January 1977 and last March, RFE said, Markov broadcast 14 programs based on his relations with Zhivkov. This series, as well as Markov's other RFE broadcasts, dealt with cultural and intellectual observations and not political matters, the spokesman said. Markov's last program for RFE, described as appealing primarily to an intellectual audience was broadcast 10 days ago.]

Markov's chief activity recently has been broadcasting on Britain's cultural scene for the foreign service of the BBC.

His final day on the job was described by Markov's fellow BBC broadcaster and close friend, Ted Lirkoff.

Thursday evening, Lirkoff said Markov had been walking along the busy Strand about 6:30 on his way to the BBC studios.

"Some man, innocently pretending, had pushed him in the leg with the point of his umbrella," Lirkoff recalled Markov had related.

"Markov said he was well-built. He told him, 'I am sorry' in a foreign accent and got into a taxi."

In the studio, Markov suddenly felt "great pain and asked me to look at his leg," Lirkoff said. "He took his trousers down and I could see an angry red spot like a pimple on the thigh of his right leg at the back."

That night, Markov's British wife, Annabel, telephoned the BBC to say that her husband was running a high fever. On Friday he was taken to St. James's hospital, still with a high temperature and vomiting small clots of blood.

Before Markov died on Monday, he told friends, "I am poisoned."

Commander Jim Nevill of Scotland Yard's anti-terrorist branch attended the inconclusive post mortem yesterday. His men are now trying to discover how Markov died. They have been joined by officers from M15, the counterespionage service of the Home Office. According to United Press International, Markov also suffered from a kidney disorder.

All during his eight years here, Markov told friends he had received threats on his life, and on the life of his brother, Nicola, who lives in Italy. Markov told his BBC superiors he feared he would be kidnapped.

Whether this was the over-worked imagination of an emigre playwright and author or whether there was substance to Markov's fright is the puzzle the security officials must solve.

Last night, they acknowledged they had little hard evidence with which to work. If the mystery is solved, they expect that, like most such cases, the answer will come from agents in Eastern or Western Europe.