The former nightclub bouncer told detectives, in a prison interview this week, that he had hidden her body in woodland 24 years ago.

Elizabeth Chau, 19, a computer studies student at Thames Valley University, vanished in west London in 1999.

Bellfield "admitted" killing her in conversation with a prison visitor last year, then wrote a confession that prompted a visit from detectives from the Metropolitan Police's unsolved murder squad.

He described how he had killed her and, using a map brought into the prison, he showed police a rough area where he had hidden her body.

Bellfield's solicitor Theresa Clark said: "He tells me he feels it's important that her family have some closure. He wants to see justice done because they have had to live this for so long and that's unfair. He gains nothing from it, there is no positive publicity for him."

Bellfield, 54, is serving a whole life sentence for the murders of two young women and the schoolgirl Milly Dowler, whose body was found buried in woodland after she was snatched from the street in 2002.

Bellfield's latest confession comes after he admitted last month to murdering Lin Russell and her daughter Megan, according to a lawyer.

Michael Stone is currently serving three life sentences in prison for the murder of Ms Russell, 45, and her six-year-old daughter who were found bludgeoned to death in Chillenden, Kent, in July 1996.

Ms Russell's other daughter Josie, then aged nine, suffered severe head injuries but survived.

Stone has always protested his innocence over the attack.

Bellfield claimed responsibility for the Chillenden murders last year but later retracted the statement.

Stone's solicitor Paul Bacon said Bellfield has since written and signed a fresh confession, adding the move "must have taken some courage and considerable soul-searching".

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Bellfield was given a whole life term for murdering 19-year-old Marsha McDonnell in 2003 and 22-year-old Amelie Delagrange in 2004, as well as trying to murder 18-year-old Kate Sheedy in the same year.

He was already serving his sentence when he went on trial for killing 13-year-old Milly Dowler, who was snatched while walking home from school in Walton-on-Thames, Surrey, in March 2002.

Bellfield was found guilty of abducting and killing the schoolgirl following a trial at the Old Bailey in 2011.