The families of those killed in an RAF Chinook crash in 1994 have urged Andy Burnham to end Britain’s “cover-up culture” and order an independent review into the disaster.

Twenty-nine serving military personnel died when the Chinook HC2 helicopter crashed on the Mull of Kintyre in south-west Scotland during a flight from Northern Ireland.

The two pilots were initially blamed for the crash but exonerated after an inquiry in 2011, which did not determine its cause.

Liam Fox, the former Conservative defence secretary who ordered that official review, said last month there were now “deep concerns” that “vital information” could have been withheld.

Fox, who is backing the calls for a fresh independent review, said there was now a “strong enough belief” that a deliberate cover-up had taken place. There were concerns, he said, that details provided by the Ministry of Defence (MoD) on the airworthiness of the Chinook that crashed were “not correct”.

A high court judge ruled this month that the families of several victims of the crash could not bring a legal claim against the MoD over the incident because it had been brought too late.

The Chinook Justice Campaign (CJC), which is made up of more than 55 family members of 25 of the victims, said it would take the case to the European court of human rights.

However, Matt Tobias, whose father, Lt Col John Tobias, was killed in the crash, said the families “do not want years of further litigation” and urged the prime minister to help by ordering a fresh independent review.

He said: “We would urge Mr Burnham to meet us within his first 100 days in office so we can present the evidence that has emerged over recent years and explain why we believe a fresh review, independent of the Ministry of Defence, is now essential.

“Mr Burnham’s speech in the House of Commons, in which he spoke about ending Britain’s cover-up culture and strengthening the duty of candour, gave our families real hope.”

In a letter delivered to Burnham, the Chinook families said it could be a “test case” for the new Hillsborough law, which was unanimously backed by MPs this month and creates a legally enforceable duty of candour compelling public officials and authorities to act transparently during investigations.

Tobias said: “We ask that he and his ministers give the Chinook families more respect than we received from his predecessor, who denied us a meeting and an inquiry – believing MoD lies instead. After 32 years, we are not asking for special treatment. We are simply asking for the truth.”

The CJC group said it wanted Burnham to establish a fresh review, independent of the Ministry of Defence, with full access to all relevant documents relating to the airworthiness of the Chinook helicopter and the circumstances leading up to the crash.

An MoD spokesperson said: “Our thoughts and sympathies remain with the families, friends, and colleagues of all those who died in the Mull of Kintyre crash.

“We understand the recent court judgment will be disappointing for those involved. Defence Ministers have previously met with the CJC and we will continue to engage to hear concerns and discuss this important matter.”