New research shows an apparent link between British nuclear tests in the South Pacific in the 1950s and genetic defects seen in veterans.
Servicemen claim they were not given adequate protection
Massey University in New Zealand said changes to veterans' chromosomes could be attributed to their participation in the tests at Christmas Island.
Lawyers for British veterans who served there said the study strengthened their claim against the Ministry of Defence.
The MoD, which has denied the claim, said it would review the new findings.
More than 700 veterans - 400 from the UK and 300 Commonwealth colleagues from New Zealand and Fiji - are currently in the middle of legal proceedings to claim compensation from the UK government.
Many of them have claimed they were not given suitable protective clothing during the detonation of nuclear devices in the testing - codenamed Operation Grapple - between 1952 and 1962.
Rosenblatts, the London legal firm acting on the veterans' behalf, claim the troops were exposed to significant doses of radioactive material, which has directly led to many of them contracting severe illnesses including cancers.
The study by Massey University was carried out on 50 of the New Zealand military personnel who took part in Operation Grapple.
DNA tests discovered they had a much higher than expected level of translocation - a chromosome defect which can lead to cancer and other illnesses. The scientists concluded that the probable cause was radiation exposure.
Rosenblatts is now calling for similar tests to be carried out on the veterans from the UK.
Clive Hyer, the senior supervising partner, said: "The case is progressing and we are extremely pleased with the outcome of this report. This is the last piece of the evidential jigsaw puzzle that we needed."
A spokesman for the Ministry of Defence said: "The Ministry of Defence remains open to new scientific or medical evidence concerning nuclear test veterans and we are reviewing the findings of this latest study.
"Previous independent reports have concluded that there is no evidence of excess illness or mortality among the veterans as a group which could be linked to their participation in the tests or exposure to radiation."