Ten former servicemen sought damages from the ministry, arguing that a low but significant dose of radiation during nuclear testing in Australia and on Pacific Ocean islands in the 1950s resulted in illnesses including cancer, skin defects and arthritis.

But the Court of Appeal said nine out of the 10 test cases cannot continue in court, because the veterans launched the cases after the legal time limit expired and because the men could not prove that radiation — rather than the onset of old age — prompted their illnesses.

“We have no doubt that it will appear that the law is hard on people like these claimants who have given service to their country and may have suffered harm as a result,” Judge Janet Smith said in the judgment. She noted, however, that veterans exposed to radiation that might have caused them injury are entitled to a war pension.

The 10th case, that of Bert Sinfield, was entitled to proceed to trial. Sinfield, who died in 2007, claimed damages for anemia and lymphoma. The 10 were test cases among a group of 1,011 veterans — most from Britain, though some are from Fiji and New Zealand.

Neil Sampson, a lawyer representing the veterans, said attorneys are considering taking the nine rejected cases to the Supreme Court.

He added that because the 1,011 cases were all different, there was nothing to stop the others from suing.

Defense officials argued that the ministry took all precautions to protect servicemen from radiation exposure.

It also said that in most cases, the men were exposed to no more than the background radiation they would have experienced in the UK.