A 26-year-old man has been arrested on suspicion of murder of the woman in the Ifield murder inquiry.
Sussex Police was called to a Volkswagen Jetta car which had been set on fire parked close to Ifield Golf Club in Rusper Road, Ifield, at around 2.30pm on Friday (March 13).
A spokesman said: “When fire crews attended, they found a body in the boot of the car, which had suffered extensive fire damage.
“A post mortem has revealed the body is that of a woman possibly aged in her 20s.
“The cause of death has been given as smoke inhalation.”
The man from London was detained on Tuesday (March 17). He is now in custody awaiting questioning.
Officers are still trying to identify who the woman is.
Anyone who has any information about her identity is asked to contact police on 101 or email email@example.com Operation Maderia or ring the independent charity Crimestoppers anonymously on 0800 555111.