The woman who was found dead in Gerrards Cross, Buckinghamshire, on Tuesday (June 23) was from Hayes.
While formal identification has yet to take place, the woman is believed to be Anita Kapoor, aged 34, from Hayes.
Next of kin have been informed and specialist officers are supporting her family at this difficult time.
A post mortem was carried out on Wednesday (June 24) and cause of death has been given as asphyxiation, due to compression of the neck.
On Tuesday, officers arrested a 50-year-old man, also from Hayes, on suspicion of murder.
He has since been released without charge.
Speaking on Wednesday, Det Supt Gill Wootton said: “We would like to speak to anyone who recognises Anita and knows of her whereabouts between 3am on Tuesday, when she was last seen in Oswald Road, Southall, and 8.36am yesterday when her body was found in Gerrards Cross.”
“When last seen, she is believed to have been wearing a black, thigh-length coat with zips at the sides, black tracksuit bottoms with white writing down the sides, elasticated at the bottom and white, Reebok trainers.
"We would appeal to anyone who has knowledge of Anita or her movements in the early hours of June 23 to contact the investigation team.
“We would also ask that anyone who was driving past the lay-by on the A413 Amersham Road during the early hours of yesterday morning and saw anything suspicious and has not yet been in touch with the police to call us as a matter of urgency on 101.
“Our priorities are to identify and arrest those responsible for Anita’s death and support her family at this difficult time. The family of Anita have asked that the media respect their privacy at this difficult time.
“Thames Valley Police are working with their counterparts in the Hillingdon and Ealing boroughs of the Metropolitan Police, both in terms of the investigation and also the protection and reassurance of local communities in both force areas.”
Supt Yvette Hitch, LPA Commander for Chiltern and South Bucks, said: “We would like to thank the local residents and community in Gerrards Cross for their patience as officers work to establish the circumstances surrounding the death of Anita Kapoor.
“The scene watch is still on at the scene and the lane on the A413 Amersham Road remains closed. This is expected continue for the next couple of days.
“Officers from the local Neighbourhood Team continue to make house to house enquiries and patrolling locally to provide reassurance. If anyone has any concerns, please feel free to approach an officer."
If you do not want to speak directly to the police you can contact the independent charity Crimestoppers anonymously on 0800 555 111. No personal details are taken, information is not traced or recorded and you will not go to court.