Mr Allason, who writes under the name Nigel West, bases his allegations on the recently released "Venona" decrypts of Soviet diplomatic traffic.
Venona was the name given to the file of some 2,000 intercepted Soviet cables between Moscow and its intelligence officers at embassies and consulates in Washington, New York and London between 1940 and 1948. Decoders in the US National Security Agency and Britain's GCHQ worked for years to unravel the contents, and the results of their work were made public by the National Security Agency in 1995.
Rudolf Peierls, knighted in 1968, was born in Berlin in 1907 and died in 1995. He came to Britain in 1933 to escape the anti-Jewish excesses of Germany's new Nazi regime. He became professor of physics at Birmingham University, where he worked until the outbreak of war with the equally distinguished Otto Frisch.
Sir Rudolph and Professor Frisch compiled a historic memorandum to the British government's top secret "Maud Committee" describing the possibility of a uranium bomb. As a result, both worked on the early "Tube Alloy" British bomb project and later transferred to the hush-hush US Manhattan Project at Los Alamos.
In 1931 Sir Rudolph had married Genia Kannegisser, a Russian student he met at a conference in the Soviet Union. He managed to get her out of the country and they settled in England in 1933.
Mr Allason says the agents referred to in Venona cables as "Pers" (the Persian) and his wife code-named "Tina" bear strong circumstantial resemblance to Sir Rudolph and his wife. "Pers" provided vital information about the Manhattan Project to the Soviets. But Sir Rudolf's family, friends and former colleagues have rushed to his defence.
His daughter, Jo Hookway, says Mr Allason is dragging up old allegations. Her father was awarded an out-of-court libel settlement in 1979 against the author Richard Deacon who suggested that he might have worked for the Soviet Union.
Professor Hans Bethe is outraged. "I knew Rudi Peierls from 1927 and being a spy was totally out of character for him," says the 93-year old fellow physicist, veteran of Los Alamos, Nobel Prize-winner and an emeritus professor of Cornell University, Ithaca, New York.
"The life of Rudi and Genia Peierls was an open book," he adds. "Klaus Fuchs was a man who could be a spy - he would never talk openly about his own life. But the Peierlses would talk openly to all their many friends. The allegations against them are nonsense." Mr Allason says "Pers", a partial anagram of Peierls, was in the right place at the time of key leaks of atomic information to the Soviets. He also says Genia easily obtained permission to emigrate to Germany with her new husband, unusual in Stalin's Russia.
There is no doubt the authorities harboured suspicions about Sir Rudolph. When he returned to Birmingham University in 1945 he worked as a consultant for the Atomic Energy Establishment at Harwell. But in 1957 his security clearance was withdrawn after the Americans asked for a bar on his access to their secret nuclear papers.
He resigned from his consultancy. But his academic life prospered and from 1963 to his retirement in 1974 he was Wykeham Professor of Physics at Oxford.
THE YEARS OF TREACHERY
n Kim Philby, Burgess and Donald Maclean are the three most famous members of the Cambridge spy ring. Recruited in 1930s by the Soviets while at the university. Achieved senior positions in MI6 and the Foreign Office. All fled to the Soviet Union during Cold War.
n Anthony Blunt was revealed as the Fourth Man of the ring in 1980. MI5 earlier identified, confronted but did not prosecute Blunt. He lost his job as the Queen's art adviser, and his knighthood, when his treachery was made public.
n Former Treasury official John Cairncross was the last of the ring to be publicly identified. He was revealed as the Fifth Man in the late 1980s. All the Cambridge spies are dead.
n Dr Allan Nunn May, British scientist jailed in 1946 for sending atom secrets to Russians. He is still alive in Scotland. Unmasked after GRU cipher clerk Igor Gouzenko defected in Ottawa and revealed Soviet spy operations.
n Dr Klaus Fuchs, German, emigrated to Britain and worked in America on wartime atom bomb. Early Venona codebreaking identified him as Soviet spy. Convicted in Britain in 1950 and jailed. As result of his arrest, Julius and Ethel Rosenberg were also identified as running a Soviet spy ring in the US, and executed.
n Dr Theodore Hall, American, also worked on Los Alamos atom bomb project. Recently confessed to having been a Soviet spy. Venona codename "Youngster". Now retired and living in Cambridge.