A sexual predator has been convicted of murdering a “trusting and friendly” mother in her home more than 36 years ago after being snared by a “one-in-a-billion” DNA breakthrough.

Convicted rapist Graham McGill 59, was an inmate at HMP Edinburgh on temporary release in 1984 when he strangled Mary McLaughlin, 58, in Partick, Glasgow.

The mother-of-11 had enjoyed a night out drinking and playing dominoes at different bars on Wednesday September 26 of that year and was last seen at around 10.45pm leaving to go to a chip shop on her way home.

Jurors convicted McGill on Friday at the High Court in Glasgow of murder after deliberating for just over two hours.

The trial has heard Ms McLaughlin was throttled with the cord of her own dressing gown.

McGill, who has sat quietly hunched over in the dock since the trial began on Tuesday wearing the same light-blue rain jacket, made no reaction as he was convicted.

Jurors removed a reference in the charge that the former welder had taken off Ms McLaughlin’s clothing with intent to rape.

Martin Cullen, 60, one of Ms McLaughlin’s sons, said he is relieved his mother has got justice and gave a thumbs up to reporters as he left the court on Friday afternoon.

Ms Mclaughlin’s death sparked a major police investigation and spawned dozens of lines of inquiry, but the cold case remained unsolved until modern DNA techniques placed McGill in her flat with a greater than billion-to-one likelihood, the trial heard.

DNA found on her dress, inside the knot of the dressing gown belt, a cigarette end, and on a black bra all matched McGill, forensic scientist Joanne Cochrane told jurors.

McGill’s ex-wife Suzanne Russell also told jurors that in 1988, he had confessed to murdering a woman because he “just wanted to know what it felt like”.

She told the court: “He said he was shocked at how long it took to actually murder her.

“I didn’t believe him… he was threatening me because he didn’t want me breaking up with him.

“He said if I ever told anyone he would kill me. He said if I ever repeated it or ever tried to leave him, that’s what would happen.”

Ms Russell added that McGill said was not worried about being caught by police “because she was on her own, she didn’t have anybody and she was more like a prostitute”.

McGill, who was not known to the area, was convicted in 1981 of rape and jailed for six years at HMP Edinburgh but was on release as part of a “Training For Freedom” initiative, police said at a briefing before the trial.

McGill was also sentenced to life in 1999 for an attack on a woman but released on licence in 2007, the court heard.

The previous convictions were not shared with jurors hearing the case.

Judge Lord Burns said he would sentence McGill on May 18.

McGill was released from his first sentence on October 5 1984, just three days after Ms McLaughlin’s remains were discovered by her son Mr Cullen.

Mr Cullen told the trial how he kicked her door down after detecting “the most horrible smell you will smell in your life” coming from her third-floor flat in Crathie Court in Laurel Street.

He said: “My partner went in and came out screaming. I went to the end of the hall and I could not go any further.”

Graphic video of the scene showed her lying on her back in a green dress – worn back to front – with her right arm hanging down the side of the bed and her legs apart.

The trial heard Ms McLaughlin was well-known in the Partick area, was unemployed, had previously gone by the surnames Cullen and Mullen, and had 11 children by two different partners.

Prosecutor Alex Prentice QC said: “You might form the impression she was someone perhaps a little lonely, someone who would go out and meet with people to gain some happiness in her life.

“People went back to her flat, it was part of her trusting nature.”

McGill was arrested by officers in Glasgow in December 2019 and charged after a police interview.

Detective Superintendent Suzanne Chow has told reporters McGill was “shell-shocked” and “certainly wasn’t expecting the police to be chapping on his door”.