When 14-year-old Elsie Frost was murdered in an unexplained, violent attack on a Wakefield towpath in 1965, her family were thrown into a period of intense shock and grief. For Elsie’s younger brother, Colin, and her elder sister, Anne Cleave, those feelings have never faded away, but the passage of 50 years has allowed many of the unsolved questions about the murder to clarify in their minds.

This summer, hundreds of strangers across Britain have joined renewed efforts to find out what happened to Elsie Frost in broad daylight that October Saturday afternoon. An investigation into the “cold case” carried out by BBC radio journalists has caught the imagination of listeners and is giving birth to new theories. West Yorkshire police have agreed to review the evidence.

“I want to thank listeners for the feedback,” Colin said last week. “It has made us realise we are not alone on this. It has been quite emotional, and these are very rapidly moving sands.”

Listeners to Radio 4’s Saturday early morning programme iPM, sister of the weekday PM show, have heard a series of bulletins on the progress of research carried out by the show’s producers and journalist Jon Manel. So far they have established an earlier time of death and the existence of five closed files on the case at the National Archives in Kew.

Social media commentators and Twitter users have described coverage of the case as “mesmerising” and “compelling”, and several crime-solving websites have taken up the cause. The growing public interest mirrors the popularity last year of the American Serial podcasts, hosted by Sarah Koenig, about the 15-year-old homicide conviction of teenager Adnan Syed, and it has prompted the BBC to release the iPM episodes as separate podcasts this weekend and to set up a website page devoted to the case.

The fatal stabbing happened as Elsie returned home from an afternoon’s sailing practice with a club using a lake in a neighbouring disused quarry. Her body was found by a man out walking with his young children. No one was convicted of the crime, although one suspect was charged following the coroner’s inquest. The subsequent trial fell apart in early 1966 because of a lack of evidence.

“Elsie was a bright girl and very, very pretty,” Anne Cleave has recalled. “I feel she would have outshone both of us.” Her brother told listeners that he thinks of his lost sister every time he ties his shoelaces because she taught him how to do it in their kitchen that autumn, when he was six. He has painful memories of the police arriving at the house to deliver the bad news.

Manel, who admits that he is now obsessed with the case, aims to find out whatever he can and to follow all leads. It is not an attempt to solve the crime. “When Anne came to us, we said we would start trying to speak to as many people as we could. We will go wherever it takes us, but I have no idea where that will be,” he said.

Although Manel and his colleagues have editorial control, Colin and Anne are forewarned about the content of each update before it is aired. “I speak to them several times a week and they understand that one day we might end up broadcasting something they don’t like. Our results are coming to us in real time, just as they did for Koenig on Serial, but our listeners are able to contribute as well as to comment on it,” said Manel.

A crime scene reconstruction of the murder of 14-year-old Elsie Frost in Wakefield in October 1965. Photograph: Peter Price/Mirrorpix

Inspired by the radio reports, several listeners have made independent freedom of information (FoI) requests for documents held in secrecy until 2030 or, in the case of one file, 2060. This is not unusual in a murder case, where files are protected because they contain personal information about people surrounding the case or because their release could hamper any future police investigation.

Yesterday, in a decision taken by Anne and Colin “out of respect for Elsie’s dignity”, the pair announced that they had withdrawn their own FoI request. They were prompted by fears that the details of their sister’s death would become accessible to a wider public, but they are already wondering if they should reverse that decision.

“In a few months we have gone a long, long way,” Colin told presenter Eddie Mair. During that time the former local MP, David Hinchliffe, has come forward to speak about his memories of the case and its impact on Wakefield. He was interviewed by police as a 16-year-old and questioned about a sheath knife that he owned, a weapon common among boys at the time. The mood in the town changed with the murder, he believes, and the shadow has never quite lifted.

He has since talked with Anne and Colin about plans to commemorate the 50th anniversary of their sister’s death this October. They hope to release 14 white doves, one for each year of her life.

The BBC investigation has also revealed that Elsie’s clothes were offered back to the family and subsequently destroyed. As a result, there is little hope for a forensic breakthrough.

The inquest file uncovered by Manel has also provided a contemporary account given by Elsie’s sailing instructor, John Blackburn, who told police he was out on the lake with her until shortly before her body was discovered.

Anne said last week that thinking again about the crime had been difficult after years spent trying to distract herself. She is driven, though, by a need to answer some of the questions. “It is not about retribution,” she said.

Manel believes his work on the case is as much about the impact of the crime on the family and the town as about finding a murderer. “People quite often ask me now where this will end, and the truth is that we don’t know.”

The influential Serial podcast, which became one of the most widely downloaded English-language programmes of all time, certainly made a difference to the safety of the conviction against Syed for murdering his ex-girlfriend, Hae Min Lee, in Baltimore, Maryland. Public interest in that unfolding case, coupled with the work of Koenig and her radio team, led to a formal review of the case, which is due this summer.