Miller is building the firearms centre as part of a £102m PFI scheme that also includes new custody and crime investigation centres.
Multiple fire crews spent hours fighting the fire at the police training centre, which is under construction near to - but not on the same site as – the police headquarters.
The alarm was raised shortly after 04.30hrs. When crews arrived, they found around 50% of the building – which measures around 140m by 40m – was well alight.
Avon & Somerset police’s assistant chief constable Dave Hayler said: "This is a very sad day for us. We're devastated to see the impact of the fire. The training centre is a new state of the art development designed to train firearms officers across three forces. For the communities of Avon and Somerset, Gloucestershire and Wiltshire whose officers will be trained there, it's a tragic setback.
"The damage is extensive and we'll be working closely with fire investigators and our own forensic teams to understand what happened to cause such a large fire. The fire service will be on site for some days to come until they're absolutely satisfied that any danger of the fire relighting is exhausted.”
The new training centre at Black Rock Quarry near Portishead will provide the three police forces with a hub for firearms training including self-contained and enclosed indoor firing ranges plus a tactics enclosure together with staff offices, training facilities, and other related services.