West London relatives of servicemen who died of cancer after witnessing nuclear tests in the 1950s are calling on the British government to join its allies in offering compensation.

Veterans' families in Shepherd's Bush, Hammersmith and Chelsea are supporting a campaign by more than 1,000 former armed forces personnel, widows and children for recognition of the damage caused by atomic bombs detonated in the South Pacific after the Second World War.

Allies including the USA, Canada and France have acknowledged the link between nuclear tests and cancer in those who witnessed them at close hand, many of whom were on compulsory national service, and have already paid compensation.

But the Ministry of Defence has challenged a similar campaign by British veterans, arguing that too much time has passed since the explosions for them to bring a case.

A final ruling on whether the collective claim can be heard is expected at the Supreme Court next month, and the veterans and their families are calling on the government to drop its opposition and recognise the damage caused to personnel, most of whom were given no protection against radiation.

The campaigners include the Hammersmith and Fulham-based family of Alexander Mackinnon, who was stationed on the Monte Bello islands while on national service at the age of 18, in 1956. He witnessed two atomic explosions, the staggering scale of which he described to his family before he died of stomach cancer at the age of 45.

Alan Mackinnon, of Ashchurch Grove, said: "He described the first explosion as 'a hell of a flash' even though he was facing away from it. The second explosion was much larger, resulting in a fireball which he said was 'quite beyond words' and 'terrifying'.

"It's not about the money – they will never be able to compensate us for the loss of a relative. The other countries have recognised that there is a link and have compensated their veterans. But the Ministry of Defence seems particularly determined not to give any right of recognition."

Also fighting on behalf of the Atomic Veterans group is Chelsea resident Mavice Hine, whose father, Wing Commander Thomas Hine, witnessed eight explosions while stationed on Christmas Island.

He died of pancreatic cancer in 1980 at the age of 61, and was one of many veterans who suffered ulcerated legs, a condition which his family believe was brought about by walking through radioactive water.

Mrs Hine, 66, of Cale Street, said: "I think it's disgusting how the Ministry of Defence has dismissed them all. These men were ordered to go out there - they didn't have a choice. They knew our men were going to be tortured for the rest of their lives for standing under a radiation cloud.

"It's not about the money. My dad was in Bomber Command during the Second World War, and without men like him we wouldn't have a Britain. We're really proud of what he has achieved."

The current armed forces minister, Liberal Democrat MP Nick Harvey, said in June 2009 that the UK was continuing to 'ignore her veterans and hide behind legislation' to deny the atomic veterans a fair hearing.

But the MoD continues to fight the campaign, and a spokesman said it would await the ruling of the Supreme Court in March. It will follow a previous ruling by the Court of Appeal, in November, that the veterans had not produced any evidence to link illnesses with attendance at nuclear tests.

The minister for defence personnel, welfare and veterans, Andrew Robathan, said at the time: "While I have tremendous sympathy with anyone who is ill, the court accepted arguments that the general merits of the claims were extremely weak."

He said the MoD recognised the 'invaluable contribution of all service personnel' and urged them to apply for war pensions, which are available to all those who suffer illness or injury as a result of service.