By Cara Sulieman
Sheila was brutally murdered at Gypsy Brae in the Granton area of Edinburgh just before midnight on April 7 1983.
A reconstruction of her last moments were finally broadcast on Crimewatch on Monday night after an attempt last month failed due to technical issues.
And since the show, officers say they have received 20 calls from members of the public offering information that might help them crack the case.
The appeal combined touching words from Sheila’s family with a gruesome reconstruction of the sex worker’s last known movements.
Her murderer ran her over at least once and dragged her body under the car for a “considerable distance” before driving off and leaving her for dead.
It was a CB radio enthusiast who discovered Sheila’s body after seeing headlights on the shore and going to investigate.
The clip also showed crime scene evidence of her shoes, clothes and watch, strewn across the ground
Sheila’s handbag was later discovered in a car park in East Lothian, not far from the A1.
“Funny and witty”
During the appeal, Sheila’s brave family spoke of how she was “funny, intelligent and witty,” but ended up working the streets as a prostitute.
Sister June said: “She just fell into the wrong crowd and got into drugs and these things escalate.
“It’s difficult to comprehend that she actually was working the streets and it’s so devastating to know she went down that road and did what she did.”
And her two sons, Alan and Michael, told how her murder, when they were just two and seven, had affected their lives.
Alan said: “How somebody could do such a heinous crime to such a beautiful person in such a lovely spot is beyond me.
“I’ve always felt robbed about my mum getting taken away from me.
“I would have loved to have known her better and I would have loved even more for her to still be here today.”
Michael added: “To think about how I would be with a mum is a dream; you can only dream of that, and I’ll never find out and it’s because of one person out there.
“It’s pretty much screwed me over.”
The investigation into Sheila’s murder was reopened last year when advances in technology meant that police could profile the DNA of her killer.
One of the most important leads that the police hammered home in the BBC programme was the presence of a sexually transmitted disease.
There is a 50 per cent chance that the killer contracted a disease and would have had to have treatment not long after the crime.
They are asking any suspicious girlfriends or wives to come forward.
Police are hopeful
And with such a strong response already, officers are hopeful that they will finally catch Sheila’s murderer.
A spokesperson for Lothian and Borders Police said: “Monday night’s reconstruction has prompted a great response from the public.
“There is now a lot of investigation to be done, and we are hoping these calls could provide some positive leads for the investigation.
“We would like to thank everyone who has taken the time to get in touch, and try to help us provide some answer’s for Sheila’s family.”
Anyone with any information can contact the incident room direct on 0131 221 2028, or can talk to Crimestoppers in confidence and complete anonymity on 0800 555 111.