Detectives launched a major manhunt after the grisly discovery of the remains at the bridge on Thursday after they were alerted to reports of a man with a suitcase acting suspiciously on the bridge just before midnight on Wednesday.
London's Metropolitan Police said it had now taken over the manhunt and a crime scene was in place in west London.
Police want to speak to this man after two suitcases containing bodies were found at a UK bridge. (AP PHOTO)
Police said it was believed the suspect had travelled from the British capital to Bristol in southwest England earlier that day, and had taken a taxi to the bridge with the suitcases.
"We're able to confirm forensic post-mortem examinations are still being carried out on the remains found within the two suitcases, but they are believed to be of two adult men," Acting Bristol Commander Vicks Hayward-Melen told reporters on Friday.
"It's important to stress they have not yet been formally identified and efforts to locate and speak to their next of kin are being prioritised."
Police said an initial post mortem had proved inconclusive and further tests were ongoing.
The Daily Mail newspaper reported a US tourist and his wife had been waiting for a taxi close to the bridge and had seen two men struggling to carry heavy suitcases across the road.
The couple told the paper a woman passerby had intervened to help and, querying the weight of the bags, had asked them "What's in them? Bodies?".
The suspension bridge, one of Bristol's most recognisable landmarks was built based on a design by renowned 19th century engineer Isambard Kingdom Brunel, opened in 1864.
