Colin Frost and Anne Cleave travelled to Westminster on the 53rd anniversary of Elsie’s death to personally deliver a memorandum to Attorney General Geoffrey Cox that they hope will result in the “incorrect” 1966 inquest, which blamed the killing on the wrong man, being quashed.
Mr Frost, 59, said only a new inquest would give the family “closure” in one of Britain’s longest running unsolved murder cases.
Elsie, 14, was attacked from behind and stabbed in the back and head as she walked through a railway tunnel off a canal towpath in Wakefield in October 1965.
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Detectives had been reinvestigating her murder since 2016 and were preparing to bring charges against convicted child killer and rapist Peter Pickering.
But the 80-year-old died, known as the Beast of Wombwell, died in March after being taken ill in the secure psychiatric accommodation in Berkshire where he was held for more than 45 years.
In the week before his death, Pickering was found guilty of the violent rape of an 18-year-old woman in Sheffield in 1972.
The crime only came to light as a result of the cold case investigation into Elsie’s murder by West Yorkshire Police.
The family praised the force’s work and said a new inquest was needed to air the evidence.
Mr Frost said: “The best closure would of course have been having Pickering in front of a jury and getting a guilty verdict on that, that’s what we really wanted.
“(An inquest) is the only option we’ve got now and if that comes to fruition, that will give us closure, and that’s what we need.”
Meanwhile, Ms Cleave, 71, criticised the Crown Prosecution Service (CPS) for bringing the rape case to court before charging him for Elsie’s murder “because they knew they were going to get a guilty verdict”.
“What that did in effect was it meant that it sidelined ours completely,” she said. “It isn’t just.”
A CPS spokeswoman said: “Our deepest sympathies go to the Frost family. Although we understand the sense of frustration, it is not correct to say that other charges were prioritised above Elsie’s murder.
“Investigations into all potential offences were carried out simultaneously and the CPS provided ongoing advice from the earliest stages.
“The CPS did not receive a full file of evidence for Elsie’s murder suitable for review until 30 January 2018 - around six weeks before the suspect’s death.
Wakefield MP Mary Creagh said getting to the truth of what happened to Elsie was "important not just to the family, but to Wakefield and to West Yorkshire as a region".
“People remember where they were when Elsie was murdered, she was a local girl at a local school involved in her local sailing club, she was well known and well loved," the Labour MP said.
“I think her death is unfinished business for the city and for the people of the city who grew up not knowing, and people want to know and people have a right to know - not just her family but the wider community that lost this child so tragically and so violently.”