He died in his sleep early Sunday, the newspaper quoted his editor, member of parliament Rupert Allason, as saying.
Cairncross had been living secretly in western England after returning from self-imposed exile in France six months ago to write his memoirs, the paper said.
"He suffered two strokes, the most recent only about a month ago," Allason, who also writes spy novels, said. "The memoirs were finished and they were intended for publication in March, but that may have to be accelerated now."
Cairncross, a former British civil servant, had repeatedly denied he was a member of the famous Cambridge University ring of spies, although he admitted giving information to Moscow.
"The Russians regarded him as one of their Ring of Five in London because of the quality of his information, but he saw himself as completely separate from Burgess, Blunt, Philby and [Donald] Mclean," Allason said.
"He regarded himself as having given no information that had harmed British interests and believed that he had been entirely loyal to his country."
Allason said Cairncross believed he was only passing on information that would help the Soviet Union defeat Hitler.
Cairncross had just married longtime companion Gayle Brinkerhoff, a U.S.-born opera singer, in August.
Former Soviet spy Oleg Gordievsky, who worked as a double agent for Britain before defecting in 1985, unveiled Cairncross as the "fifth man" in 1990. Three of the other four men died in Moscow -- Burgess in 1963, Mclean in 1983 and Philby in 1988. Blunt, having been exposed as a spy, died weeks after Mclean in 1983.
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