A former CID officer - believed to be the victim's partner has been arrested after the grim discovery.
Surrey police confirmed the victim as Detective Constable Heather Cooper.
Her partner believed to be Peter Foster is reputed to be a former detective Inspector recently made redundant by the Surrey police.
The house where they lived has been taped off for forensic examination which is already in progress.
Four miles away in Blackburn Woods, Near Lurgashall forensics are going on where the body was found,
Police were alerted by a 999 call they received shortly before midnight on Sunday.
A police spokesman said " Officers went to Blackdown Woods where a search led to the body."
a 35-year-old man has been arrested on suspicion of murder and is in custody.
It is undderstood Det. constable Cooper was the mother of two children - a son aged four and another child aged about 12 months.
Neighbours of the dead policewoman said she was based at Guildford.
Mr. Foster is believed to have left the force recently. He received a commendation in 2006 foir his work in a sex abuse investigation.