The police were alerted and the following morning Mrs Gregson's body was found floating in the River Aire. She had been strangled and police believe she may also have been sexually assaulted.
Yesterday detectives began reconstructing Mrs Gregson's final hours. A breakthrough in DNA analysis that has provided a genetic profile of the murderer has given the investigation fresh impetus.
The case is the latest unsolved crime to be reopened decades later because of advances in DNA testing.
It comes a day after a man was convicted in Liverpool Crown Court for the murder of Cynthia Bolshaw, 16 years after her death, on DNA evidence.
West Yorkshire police had been waiting for advances in forensic science to obtain a DNA profile from a tiny stain found on Mrs Gregson's clothing. They have refused to reveal details of the substance tested, but it is likely to be blood or semen. At the time of the murder more than 9,000 people were interviewed. The "Yorkshire Ripper", Peter Sutcliffe, was ruled out after DNA profiling in 1997.
The case was reopened in June after forensic scientists used a new technique known as SGM that allows genetic profiles to be obtained from a single cell.
Since then DNA tests have been carried out on more than 400 suspects who were questioned at the time of the murder. Police are now widening their search and are trying to track down people who have moved from the area since 1977. They are concentrating on men who were aged from their late 30s to their mid-50s in 1977. Detective Chief Superintendent Brian Taylor, who is heading the murder hunt and who worked on the original investigation when he was a sergeant, said a witness saw a man standing over a woman's body near the River Aire on the night Mrs Gregson was murdered.
In their latest attempt to trace witnesses police are using a model to re-construct the final hours of Mrs Gregson's life. The film is expected to be shown in the New Year on BBC1's Crimewatch UK.
Det Ch Supt Taylor said that the murder shocked the tight-knit community of Shipley, where Mrs Gregson had lived in a canal-side cottagewith her 50-year old husband, Bill, and their son Michael, 11.
Mr Gregson died in 1981 from a heart attack. Their son still lives in the area. Det Ch Supt Taylor said: "We hope that by reconstructing the events just prior to Mary's death will help jog some memories."
He added: "We have been waiting for advances in the technology of DNA. We had tested a sample obtained from clothing, but it did not produce a profile."
Police are particularly keen to find a man who in 1977 was described as being in his mid-20s, about 5ft 10ins with a long face, a thin nose, lightish brown hair, light coloured eyebrows and a bad complexion.
In August, police revealed that using a new DNA profile they had discovered the identity of the man who killed a pregnant woman 30 years ago. But the murderer of Rita Sawyer, 18, whose body was found in a field near Chesterton, Warwickshire, in September 1970, had already died. Police obtained a DNA sample from the dead man, who had been questioned originally with some 2,600 people.
Hundreds of unsolved murders, rapes and other cases are being reopened thanks to new investigative and DNA analysis techniques.
Forensic scientists can now provide DNA profiles of criminals from a single blood cell, a sperm or even from a flake of skin.Reuse content