Angela Rayner has promised to do “everything within my power” to help nuclear test veterans access their medical records.

The deputy Labour leader said it was “disgusting” that veterans and their descendants had been denied the results of blood tests from the time they served at British nuclear testing sites in Australia and Christmas Island in the mid-20th century.

Speaking at a Labour Party Conference fringe event for test veterans, Ms Rayner said: “I can’t go on without saying honestly that I will look in your eyes and do everything I can to make sure we give you what you want.”

John Morris, an 86-year-old who was sent to Christmas Island during his national service in the 1960s, told the same event he wanted four things from a future Labour government.

These included a full inquiry into “blatant disregard for the duty of care” by the Ministry of Defence; the provision of “true medical records” for all nuclear test veterans; compensation for those affected; and the passing of a “Hillsborough law” to provide legal aid funding for victims of disasters or state-related deaths.

He said: “I am talking, and have been talking, for over 20,000 men and women who are now dead and don’t have a voice.

“I am their voice. I will fight to the bitter end until we get justice for every veteran and the people overseas.”

Mr Morris and others have staged a long-running campaign after they, or their parents, were involved in the nuclear tests in Australia and the south Pacific between 1952 and 1967.

Many have suffered health problems they believe may be related to exposure to radiation during the tests, including Mr Morris whose first child died aged four months after his lungs failed to develop properly.

He has also suffered from pernicious anaemia since he was 26, a few years after he came back from Christmas Island.

He was joined at Tuesday’s conference event by Alan Owen, whose father served in the Royal Navy and was sent to assist with American nuclear tests in the Pacific; and Steve Purse, whose father served with the RAF at Maralinga in Australia during the tests.

Mr Purse was born with short stature, although doctors have been unable to diagnose the exact form he has, while Mr Owen and his family have suffered from severe heart problems.

Both men believe their fathers’ involvement in nuclear testing may have contributed to their conditions, but have been unable to access the results of blood tests carried out on their fathers by the Ministry of Defence.

All three men are now part of an attempt to sue the MoD for access to those records, which they claim have been illegally withheld.

The MoD insists that “no information is withheld from veterans”, something the campaigners deny is the case.

Mr Owen said the group decided to start a crowdfunding effort to pay for their legal case after veterans minister Johnny Mercer told them the only way to access those records was to sue the Government.

He said Mr Mercer had subsequently refused to engage with his group, Labrats, adding: “That’s no way to be a veterans minister.”

A Government spokesperson said: “We are grateful to all service personnel who participated in the British nuclear testing programme and contributed to keeping our nation secure, and are pleased that they will now be receiving a medal in recognition of this.

“It remains the case that no information is withheld from veterans and any medical records taken either before, during or after participation in the UK nuclear weapon tests are held in individual military medical records in the Government’s archives, which can be accessed on request.”