New DNA evidence has linked two murder victims 32 years after their deaths.
Officers are reinvestigating the murders of 16-year-old Hounslow schoolgirl Lynne Weedon and Eve Stratford in Leyton in 1975.
Lynne's mum, Margaret, has made an emotional appeal for information about her daughter's killer.
The 75-year-old said: "You think your memories are buried deep down, but they come back to sit on your shoulder - not a day passes without a thought of Lynne going through my mind, even after all this time."
She added: "The world is a very different place now and we had our doubts over the wisdom of spending time and money on investigating something which happened all that time ago - but it would be very satisfying to have a final closure to the events of 1975 and to know what happened and why. We appreciate the efforts, the understanding and sincerity of the current investigation team."
Lynne was raped and murdered near her home shortly after 11pm on September 3, 1975.
She had been on her way home after an evening out with friends.
Detectives believe she was followed on foot from Great Western Road into an alleyway called The Short Hedges were she was hit with a blunt object and thrown over a fence into the grounds of an electricity substation, where she was raped.
Lynne never regained consciousness and died at West Middlesex Hospital a week later.
The cause of death was a single blow to her head which smashed her skull.
The weapon was never recovered.
Her murder is now being linked to the killing of 22-year-old Eve Stratford on March 18, 1975.
Eve, who worked as a Playboy bunny girl, was last seen walking near her home in Lyndhurst Drive, Leyton.
At around 4.30pm a neighbour heard the voices of a man and a woman having a conversation.
A short while later the witness remembers hearing a loud thud coming from Eve's first floor flat.
Her body was discovered by her boyfriend at 5.25pm.
She had a nylon stocking tied round one ankle and a scarf round her hands. Her neck had been cut between eight and 12 times.
A postmortem examination at Walthamstow mortuary gave the cause of death as knife wounds to the throat.
Officers from the Met's Murder Review Group conducted a re-examination of Lynne's case - leading them to discover a DNA profile which matched Eve's murder.
Detective Chief Inspector Andy Mortimer, from the Homicide and Serious Crime Command, said: "Advances in forensic science mean that we are able to re-look at certain older cases with the very real possibility that some progress can be made that would not have been possible previously.
"As a result we now have a DNA link between the murders of Eve and Lynne, who was just 16 at the time of her death. We believe the killer could have confided in someone over the years about what happened or might even have bragged about the murders.
"They have kept a dark secret for the last 30 years and I'm sure they would have felt the need to share this burden with someone. We appeal to anyone who feels that they might have some information, however seemingly unimportant, to come forward."
A detailed review of both cases is due to be featured on the BBC's Crimewatch tomorrow.
D Chief Insp Mortimer added: "It is also possible that the killer knew his victims - this seems more likely in Eve's case due to the circumstances of her death. There were no signs of forced entry and Eve had a huge circle of friends and acquaintances. In particular I would appeal to anyone who has information about any relationships that Eve may have been involved in at the time.
"We also think that whoever was responsible had a knowledge of the Hounslow area. The killer probably knew the alleyway and the substation which provided the ideal environment in which to carry out such an horrendous crime without being seen or heard very easily."
Anyone with information should call 020 7321 7228 or Crimestoppers on 0800 555 111.