The families of those killed in the RAF Chinook crash of 1994 are calling for new Prime Minister Andy Burnham to order a fresh, independent review into the tragedy.
They also want Mr Burnham to meet with them during his first 100 days in office.
Earlier this month, a High Court judge ruled that the families of several victims could not launch legal proceedings against the Ministry of Defence over the crash.
Twenty-nine serving military personnel died when the Chinook HC-2 helicopter crashed into Scotland’s Mull of Kintyre in foggy conditions on 2 June 1994.
They had been flying from RAF Aldergrove in Northern Ireland, en route to Inverness.
The majority of those on board were British intelligence experts from MI5, the British Army, and the Royal Ulster Constabulary.
The 2011 Mull of Kintyre inquiry overturned an initial decision to blame the pilots for the crash. However, it did not determine the cause of the tragedy.
The Chinook Justice Campaign (CJC), which is made up of more than 55 family members of 25 of the victims, sought to challenge the MoD’s “ongoing failure” to set up an “independent and effective investigation” into the crash.
However, a High Court judge’s ruling threw out the case as the claim had been brought too late.
The CJC legal team has said it will take the case to the European Court of Human Rights, but Matt Tobias, the son of Lieutenant Colonel John Tobias who was killed in the crash, said the families “do not want years of further litigation”.
Mr Tobias said that Mr Burnham “has the power to prevent that” 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.
“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 has said that it wants Mr 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 Mk2 helicopter and the circumstances leading up to the crash.
In the letter delivered to Mr Burnham, the Chinook families said: “Throughout your career you have argued that the State should never use its power to frustrate families seeking the truth.
“We respectfully suggest that the Chinook case now presents the first opportunity for your Government to demonstrate those principles in practice and should be the test case for [the] Hillsborough Law.”
The Hillsborough Law was unanimously backed by MPs in the House of Commons earlier this month.
It would create a legally enforceable duty of candour which compels public officials and authorities to act transparently when investigations and inquiries take place.
The families have requested that victims minister Alex Davies-Jones, who was re-appointed last week, take up their case as one of the test cases for Hillsborough Law.
Their appeal is being backed by former Conservative defence secretary, Sir Liam Fox, who has also written personally to Mr Burnham urging him to resolve the case.
The Chinook Justice Campaign has also written to new Defence Secretary Wes Streeting urging him to “begin correcting the mistakes of your predecessors”.