James Warnock - who has been convicted of the 1982 rape and murder of 17-year-old Yiannoulla Yianni - was snared by police after he was arrested for possession of vile child pornography.
When he killed the teenager, Warnock was 22 and married.
He will be sentenced on Monday after a jury at the Old Bailey convicted him of rape and murder.
After being convicted of murder, Warnock admitted six charges of possession and distribution of indecent images of children.
The murderer will be sentenced on Monday.
He claimed to have had a summer fling with the victim - a statement branded an “insult” to her memory by prosecutors.
Warnock lived in Adelaide Road, close to the victim’s Belsize Road home, when he killed her.
When interviewed by police, he claimed to have been “popular with the ladies”.
He said of meeting Yiannoulla, who he referred to as Yuli: “We hit it off really big time… lovely smile, yeah, a really nice girl, really, really lovely girl…”
Despite high-profile appeals after the murder, Warnock cliamed not to have known the teenager had died.
He was arrested for the murder on December 30 last year after police obtained his DNA.
Detective Inspector Julie Willats, who became senior investigator on the case three years ago, said: “Advances in DNA testing had finally given us a profile of Yiannoulla’s killer in around 2003 but there were no matches on the database.
“Because there was no forced entry, it was thought Yiannoulla knew her murderer and detectives went to Cyprus to speak to her extended family to see if they could provide any useful information.
“Several pieces of hair were found on her body - we thought maybe her killer was a hairdresser. However, all these enquiries came to nothing.”
He recalled: “I was at the theatre with my mother when I had a text come through to say we had a DNA match. I found it very difficult to sit still through the rest of the performance after that.
“Warnock was interviewed and came out with his story which we then had to disprove, gathering evidence to show he was lying.
“We reviewed press coverage from the time of the murder to the present day so we knew exactly what information was in the public domain. “We could then show that all the details he was telling us about the girl he claimed he’d had an intimate relationship with were in fact already well known. He had, after all, nearly 34 years, to construct his account.”
And he said of Warnock: “He came across as a bit of a ‘Jack-The-Lad’, and a very confident liar.
“His body language was telling - he got fidgety when asked for details of his sexual relations with Yiannoulla.
“But mostly he just seemed like a normal, fairly non-descript bloke. It struck me in court when a witness described the man on the doorstep as ‘cocky’ and I remember thinking, that’s him - he thought he was irresistible like John Travolta.
“The e-fit from all those years ago - with the moustache removed - was as close a match as you could hope for how Warnock looked in 1982, with dark, swept-back hair.”
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