Radiation hurt Blair, says doctor.
A Blair spokeswoman dismissed the allegation.
Mr Blair was aged three and living with his family in the South Australia state capital, Adelaide, when the British detonated a third atomic device in the Maralinga desert region 350 miles to the north on October 11, 1956, The Bulletin magazine said.
An unanticipated wind change blew the radioactive cloud toward Adelaide.
British medical researcher and toxicologist Dick van Steenis told the news magazine that the death of Blair's mother from thyroid cancer could have been caused by the family's exposure to the radioactive fallout.
'Adelaide in South Australia was plastered with radioactive fallout from 11 to 16 October, 1956,' van Steenis said. 'As a youngster in Adelaide drinking local milk, Tony Blair is very likely to be at risk of bone cancer himself.'
A Blair spokeswoman dismissed the theory.
'It sounds like the silly season's been going on a little bit longer than we thought,' she said. 'The prime minister's perfectly fine.'
Blair's mother, Hazel Blair, died 19 years after the blast following a long battle with thyroid cancer.
Van Steenis said the prime minister would not acknowledge the impact of the bomb testing on his family because his Government could be sued by former servicemen involved in the nuclear tests.
'He has never denied that radioactive fallout in Australia was ultimately the cause of his mother's death,' van Steenis said. 'But he won't acknowledge it because to do so would strengthen the legal case against his Government for the compensation entitlements of British and Australian servicemen involved in the British atomic testing programme.'