UK police on Saturday arrested a man after two suitcases believed to contain the remains of two men were dumped on a famous bridge.

The suitcases were discovered on Wednesday after police got a report of a man behaving suspiciously on the Clifton Suspension Bridge in Bristol, southwest England.

"Detectives have arrested a man in connection with an investigation into the discovery of human remains on Clifton Suspension Bridge," said the Metropolitan Police.

The 24-year-old suspect was detained in Bristol and will be taken to London for questioning later on Saturday.

"Police are not looking for anyone else in connection with the incident," they said.

The Metropolitan Police said the victims have not been formally identified, but both are believed to be men.

The London-based force took over the investigation after evidence suggested that the wanted man had travelled to Bristol from the UK capital earlier on Wednesday.

The Clifton Suspension Bridge, designed by the pioneering engineer Isambard Kingdom Brunel, is one of the oldest surviving suspension bridges in the world.

Opened in 1864, the bridge over the Avon Gorge is one of Bristol's top tourist attractions and a symbol of the city. (AFP)