Douglas Hern, litigation secretary of the British Nuclear Test Veterans Association, said he hoped the government would now negotiate a settlement rather than appeal against the ruling.
Hern, 73, blames the death of his 13-year-old daughter from cancer on his radiation exposure.
He said that if the litigation continued without settlement many ex-servicemen would not live to see the eventual outcome.
The opposition Liberal Democrats hailed the court ruling and called on the ministry to end its "penny-pinching" treatment.
"Other countries from the US to China compensated their test veterans years ago," Nick Harvey, the party's defence spokesman, said.
"It is scandalous that the government has continued to shirk its moral responsibilities for so long."
The servicemen say the government was aware of the health risks they were exposed to and failed to adequately protect them.
The ministry denies there is enough evidence to support the claim there is a causal link between illnesses the workers suffered and their old jobs.
It said it was disappointed by the ruling and would review the full judgment before deciding how to proceed.
Servicemen from Australia, Britain, New Zealand and Fiji were involved in the tests.
In March, France announced it would compensate victims of nuclear tests carried out in Algeria and the South Pacific, after a decades-long campaign by veterans.