70-year-old John Cannan was jailed in 1989 for the rape and murder of a different woman, newlywed Shirley Banks, from Bristol.
He was the prime suspect in the unsolved murder of 25-year-old Ms Lamplugh from East Sheen in 1986.
The 25-year-old disappeared after allegedly meeting a “Mr Kipper” in Fulham for a house viewing and her body has never been found.