The family of a British girl who disappeared in Australia more than 50 years ago has threatened to name a key person of interest unless he comes forward to answer their questions.

Authorities believe three-year-old Cheryl Grimmer was abducted from Fairy Meadow beach in Wollongong in January 1970.

A suspect was charged with her abduction and murder, but his 2019 trial collapsed after a detailed confession made when he was a teenager was ruled inadmissible. He denies any wrongdoing.

Known only as Mercury, the man's identity is protected as he was a minor at the time, but a politician has offered to name him under parliamentary privilege as the family pushes for a fresh investigation.

[Mercury]'s got until Wednesday night, Cheryl's brother Ricki Nash told reporters on Friday.

Jeremy Buckingham, a New South Wales parliamentarian who has been supporting the Grimmer family, said he's prepared to use parliamentary privilege to name the man when state parliament resumes sitting on Thursday.

Mr Nash wants Mercury to explain how he knew information contained in his confession - and if it was true or not.

Enough is enough, he said, at times on the verge of tears. We want the truth to come out.

Cheryl had been on the beach at Fairy Meadow with her family on 12 January 1970. When the family decided to pack up, Ricki had been put in charge of his siblings and told to go to the bathroom block.

Cheryl ran giggling into the ladies' changing rooms and refused to come out. Too embarrassed to enter himself, Ricki went back to the beach to alert their mother. When they returned, 90 seconds later, the toddler was gone.

The family had only recently migrated to Australia from Bristol as so-called Ten Pound Poms.

Despite extensive searches, there were no leads. Then in 2017, a man in his 60s was charged with Cheryl's abduction and murder after officers discovered a confession made to police by a teenage boy in 1971.

A judge later ruled the confession could not be presented as trial evidence and the charges were dropped.

On Friday, the family released a document detailing the missteps they believe were made by authorities in New South Wales during the search for Cheryl, calling for more answers.

We've made various requests to NSW authorities for a fresh prosecution or a fresh inquest but to no avail, the family stated in their letter.

We feel that we have been fobbed off numerous times by the police, who say they are conducting reviews or exploring leads that make no sense to us. The incompetence and negligence in the NSW police investigation over the past 55 years is unfathomable.

NSW Police defended their conduct, stating that homicide detectives continue to investigate Cheryl's disappearance, with a A$1 million reward for information remaining on offer.

Police continue to examine every line of inquiry and search for answers into Cheryl's death, they stated.

Three potential eyewitnesses came forward after the BBC aired the Fairy Meadow true crime podcast in 2022, which has since been downloaded five million times. Their contacts were passed on to investigators.

However, the family was recently informed that a four-year-long review found no new evidence could lead to a conviction, despite the new eyewitnesses not being formally interviewed.

The family disputes this claim and conducted their own search earlier this month, hoping for breakthroughs with cadaver detection dogs. After a subsequent police search of the area returned only animal bones, volunteers were seen again in the area, collecting soil samples for further analysis.

Cheryl disappeared more than 55 years ago. It's time for answers, and accountability, the family expressed.

In response, the NSW parliament announced an inquiry into long-term missing persons cases in the state, including Cheryl's, to investigate investigation methods and possible improvements.