Human remains were found in two suitcases when police responded to a call about a suspicious driver, police said.
Gloucestershire police were called on Tuesday near Coleford in the Forest of Dean.
The vehicle was identified, a man and a woman were interrogated and then arrested, the force said.
Police believe the remains are of a woman, but forensic examinations are underway to identify the victim.
Earlier, detectives had an additional 36 hours to continue questioning the man, who is in his 30s and from Wolverhampton, and the woman, who is in his 20s and from Birmingham,
Det Ch Inspector John Turner said: “The nature of this incident is distressing and we are working tirelessly to understand what happened.
“Someone’s life has been lost and our priority is to identify the victim and get answers for their family.
“Excavations were carried out in the vicinity to gather evidence and, contrary to media reports, no vestiges were found in the course of these excavations. “
The road closures on the A4136 are expected to remain in place until Friday, officials said.