Officers are alleged to have turned down a key tip-off about a suspect just days after the 14-year-old was stabbed to death near Horbury Lagoon in October 1965.
Nobody was ever convicted of her killing.
It was only after a 2015 cold-case review into her death did officers name prime suspect Peter Pickering, who was already behind bars for stabbing and killing a girl near in Barnsley in 1972.
Shockingly, it was also revealed that the Metropolitan Police had sent a telegram to police in Wakefield, naming Pickering as a potential suspect in the days after Elsie's death.
On the basis of fresh evidence, a new inquest into her death was granted in April of this year by the High Court and a pre-inquest review hearing was held at Wakefield Coroner's Court this morning.
Kevin McLoughlin, Wakefield's senior coroner, told the hearing that despite inquests primarily focusing on the deceased rather than any potential perpetrator, he would have to "delve into the evidence to what the police knew" to gain a full understanding.
With Pickering dying in custody in March 2018 before he could be brought to court, Elsie's younger brother, Colin Frost, sees the inquest as the family's best hope of finding out exactly what details the police knew.
Speaking after this morning's hearing, he said: "We know how Elsie died, but Mr McLoughlin is going to go further, he will be looking at the information that the police had, which to us is the most important part of this inquest.
"We are now one step nearer to finding out what happened, putting the record right and righting all those wrongs."
Elsie Frost was attacked from behind and stabbed in the neck and head as she walked through a railway tunnel off a canal towpath in Horbury.
Local man Ian Bernard Spencer was wrongly named as her killer during the first inquest in 1966, but no evidence was offered and the case was dismissed.
He has since died but his son, also named Ian, is due to give evidence during the upcoming full inquest, along with Colin Frost and Detective Chief Superintendent Nick Wallen who will be representing West Yorkshire Police.
Around 12 other statements are due to be read out, most taken in 1965.
Mr McLoughlin said there had been around 900 witness statements originally taken after the murder.
He also ruled that it would not be a jury inquest and that it would take approximately two days to complete.
The date was set for Monday, November 18, 2019.