The children of men exposed to radiation while working at Sellafield have twice the normal risk of some forms of cancer.
A new study used leukaemia and non-Hodgkin's lymphoma data from between 1950 and 1991.
The cancer figures also found a disease rate 15 times higher in Seascale - a small village next to the nuclear plant.
The nuclear industry claims both figures are explained by people moving into the area from other parts of the country.
Ms Heather Dickinson and colleagues at the University of Newcastle compared 9,859 children fathered by men exposed to radiation at Sellafield, with those of 256,851 children born to other fathers in Cumbria.
She says despite the statistics, only 13 children of Sellafield workers contracted leukaemia over the 41-year period and workers now receive much lower doses than in the past.
The results, published in New Scientist, appear to support the idea put forward by the late Mr Martin Gardner, an epidemiologist from the University of Southampton.
In 1990 he suggested there may be a link between the doses of radiation received by fathers and leukaemia.
The idea was widely criticised by experts, who said population movements could account for the extra cases seen around Sellafield.
PA