The Appeal Court acknowledged the strength of feeling of more than 1,000 ex-services personnel, now mostly in their seventies, who believe they are still paying the price for radiation exposure during the tests in the Pacific and mainland Australia in the 1950s.
However, the judges ruled that the vast majority of the compensation claims against the Ministry of Defence had been brought to court too late and many veterans' arguments that the fallout caused a wide range of medical conditions were in any event "not strong".
Of the 10 "lead" cases used to spearhead the enormously costly group action, the Appeal Court's ruling means that only one – that of Hertfordshire man, Herbert Sinfield – will now proceed to a full hearing on the merits. The others will all be denied their day in court.
Lady Justice Smith said: "We recognise that these decisions will come as a great disappointment to the claimants and their advisers. We readily acknowledge the strength of feeling and conviction held by many of the claimants that they have been damaged by the Ministry of Defence in defence of their country.
"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."
But the judge said that law requires that veterans must prove not only negligence on the part of the MoD, but that radiation exposure was a probable cause of their injuries.
The judge, sitting with Lord Justice Leveson and Sir Mark Waller, observed that, regardless of the huge cost of the litigation, success in court for the veterans would have "enormous resource implications" for the MoD and Government lawyers.
She said a judge who ruled in the veterans' favour last year had "significantly and wrongly under-estimated" the difficulties their lawyers faced in proving that their medical conditions probably had their root in radiation exposure more than 50 years ago.
Mr Justice Foskett had also given too much weight to veterans' arguments that, if their cases were not given a full hearing on the merits, there would be a "perceived injustice".
Those involved include Evelyn Dickson, of Silkstone Crescent, Kettethorpe, Wakefield who claims the death of her husband Andrew aged 67 in 2006 – and health problems he suffered during his life – were down to the five tests he witnessed in 1958.
Douglas Hern, 72, from Spalding, an atomic test veteran who has played a leading role in the case, said: "I'm absolutely astounded. I don't understand it.
"Every other country has treated their veterans with respect and dignity, not contempt."