Body parts belonging to Sarah Mayhew were found in Rowdown Fields in New Addington in April.
Steven Sansom admitted murdering her at the Old Bailey this morning.
He also admitted perverting the course of justice by dismembering her body, disposing of it, and then cleaning up the crime scene.
Miss Mayhew was last seen in Sutton on March the 8th.
The cause of her death remains unknown, and her family are being supported by specialist officers.
Sansom, who was known to Miss Mayhhew, appeared by video-link from Belmarsh prison and will be sentenced at a later date.
Co-defendant, 49-year-old Gemma Watts, faces the same charges and was not asked to enter pleas.
