Survivors of Britain's 1950s atomic tests in the Pacific, who claim they suffered ill-health through exposure to radiation, have been prevented from suing the Ministry of Defence.

By the narrowest of margins – four justices to three – the supreme court ruled that their action should be time-barred because it had been brought too late.

Although the judgment relates to nine test cases, lawyers for the veterans say they will soon lodge high court compensation claims on behalf of hundreds of others, involving those who were more recently diagnosed with illnesses.

Dismissing the nine test cases, Lord Justice Wilson said: "It must be bad enough for the nine veterans together … to learn that they have lost their final round, but to learn that they lost by the narrowest of margins must make it even worse.

"Putting aside the law for one moment, all seven members of the court would wish to record their personal sympathy for the veterans."

One of the nine died last weekend. The majority of justices found that the former servicemen had been aware of their illnesses since they formed a campaign group to press for compensation in the 1980s.

The judges said that, under the Limitation Act 1980, their cases should have been brought within three years.

The Ministry of Defence has always denied liability for the veterans' condition, insisting that low dose ionising radiation could not cause such injuries. The cases, Wilson added, "rest on a false hope and should be brought to an end now and not later".

The veterans had contended that they did not have proper knowledge that their illnesses were connected to the atomic tests until medical research was published in 2007.

Wendy Brothers, 73, a veteran's widow, said outside the court: "I'm very disappointed. The MoD say that we have known about it for too long but they continue to say that nothing happened."

Rose Clark, 71, whose husband, Michael, died of bone and lung cancer in 1992, said the case had not been "about money, but getting official acknowledgement that the men had been put at risk".

She added: "I lost my oldest grandson at the age of eight through leukaemia. I believe it was due to genetic damage. Michael was 19 at the time he was on Christmas Island, and witnessed five atomic bombs.

"He said he was so close he could see the bones of the people on the beach beside him. It was like an x-ray, he said. The army simply told him to turn away when the explosion occurred."

The UK carried out 21 thermonuclear tests in Australia and the Pacific between 1952 and 1958, involving more than 22,000 soldiers, sailors and airmen. Of those, 1,011, or their surviving relatives, have lodged claims for compensation.

Neil Sampson, the solicitor representing the veterans, said the government should follow the lead of other countries and set up a "fair and just" compensation scheme.

"The approach that this government takes is to waste resources on fighting veterans rather than co-operating with them," he said. "Every other single nuclear power has established ways to recognise and compensate veterans.

"There are some things in life that are wrong. The approach of the government to this issue is one of those things."

A spokesman for the MoD said after the ruling: "The Ministry of Defence recognises the debt of gratitude we have to the servicemen who took part in the nuclear tests.

"They were important tests that helped to keep this nation secure at a difficult time in terms of nuclear technology.

"All the [supreme court] justices recognised that the veterans would face great difficulty proving a causal link between illnesses suffered and attendance at the tests. The supreme court described the claims as having no reasonable prospect of success and that they were doomed to fail.

"Where individual veterans are able to produce reliable evidence to raise a reasonable doubt that their illness is related to their service, they may be entitled to a war pension."