The discovery was made after the dog handler, on routine patrol, spotted a fire in the car park. After the blaze was put out, police found the body within the debris and launched a major investigation.
Forensic officers were called to the scene in Bath Road to search for evidence, after the supermarket was closed and the car park cordoned off by police. The body was removed from the scene and taken to the mortuary in Flax Bourton, near Bristol, for further forensic examination.
Police are appealing for witnesses to come forward if they were in the area or went through the car park in the early hours of August 7.
Detective Chief Inspector Mark Power said: "We would like to hear from anyone who was in and around the area of the Sainsbury's car park between the hours of 1.30am and 3am. The car park is quite active late at night, as people drive through to use the cashpoint or walk through as a short-cut.
"In particular, we would like to hear from you if you were driving through the car park or if you were the young couple who were spotted walking through the car park holding hands. You may hold information that would assist us in our inquiries, so I would urge you to speak to us."
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