Horrific murders of a bunny girl and a teenager will be featured on BBC Crimewatch on Thursday evening.
The 1975 killings of Eve Stratford and Lynne Weedon, of Hounslow, will be covered on the show which starts at 9pm.
The murders were linked in July 2006 after a review and advances in technology determined that the same DNA had been found on both victims.
Eve, 21, from Leyton, who worked as a bunny girl, was found with a nylon stocking tied around one ankle and a scarf around her hands on March 18, 1975.
Her neck had been cut between eight and 12 times at her flat in Leyton - and she was found by her boyfriend.
Lynne, a 16-year-old school girl had been raped and murdered after walking home from a night out with friends on September 3, 1975, in Hounslow.
She had been hit over the head with a blunt instrument in an alleyway called The Short Hedges.
She was then thrown over a fence into the grounds of an electricity sub-station where she was raped and left for dead.
Lynne's mother Margaret Weedon said: "It has been 40 years since our beautiful young daughter Lynne was violently taken from us.
"1975 seems so long ago and it is, forty years without her - a true life sentence.
"We are well aware that whoever murdered Lynne also murdered Eve Stratford.
"That young lady also had her life snubbed out. Her family have died now - another true life sentence.
"I will make a mother's plea for anyone who can tell us some information about the person who took my daughter and Eve Stratford's lives to come forward. Please, please give us some sort of closure."
Lynne was discovered by a local school caretaker.
Despite the horrific nature of her injuries, she was still alive when police and ambulance arrived at the scene.
However, she never regained consciousness and died at West Middlesex Hospital a week later on 10 September 1975.
The cause of death was a single blow to the head - her skull had been smashed with a heavy blunt instrument, which was never recovered.
In 2004 officers from the Met's then Murder Review Group re-examined Lynne's case and found a DNA profile which matched Eve's murder.
Detective Chief Inspector Noel McHugh said: "I firmly believe there is someone out there who has information about who carried out these murders.
"It's inconceivable the killer of Eve and Lynne has kept the perfect secret for 40 years. It's a heavy burden to carry and he must have let details slip over the years - maybe to a partner, a friend, even a cellmate - and I would appeal to anyone with information to contact us.
"I appeal particularly to mental health professionals and prison officers who may have received disclosures from a patient or prisoner and now having heard our appeals, believe the information they were told may be relevant.
"I am hopeful tonight's renewed appeal on BBC Crimewatch will encourage someone to come forward with information."
DCI McHugh said that it is likely the suspect for both murders is now in his 60s or 70s.
He added: "The man who carried out these murders is now of a different, older generation.
"Does he feel guilt, remorse, a need to explain what happened? Sadly Eve's parents have passed away but this man has a chance to bring peace to Lynne's mother and father, now in their 80s."
Detectives are keeping an open mind but have previously said it is possible the killer knew his victims, particularly Eve who had a huge circle of friends and acquaintances.
It is also thought the murderer was familiar with the Hounslow area - the alleyway and sub-station are away from busy areas and would have meant Lynne's screams or struggles would most likely have gone unheard.
Anyone with information is asked to call the incident room on 020 8785 8099 or Crimestoppers anonymously on 0800 555 111.
