Marsh told BBC Radio 4’s Today programme that “most seriously 12 of my brave officers have been injured, two of them seriously, doing their best to protect property and the people of Bristol from what was violent criminality and thuggery”.
He said the numbers at the demonstration “very quickly” rose to possibly as many as 3,000 people and a group of 400 or 500 “who really were intent on violence, damage and criminality started to commit crimes, damage police vehicles” at about 6pm outside Bridewell police station in central Bristol.
He described Bridewell as a neighbourhood station which is also used by police officers to protect the most vulnerable in the city.
He told the programme: “We know they have burnt out three marked vehicles, nine vehicles that are used for safeguarding the most vulnerable have also been damaged and the windows of the station have been put in.”
The chief constable said those involved in violence at the “Kill the Bill” protest in Bristol can expect “very serious consequences” as he revealed five arrests had been made so far.
He told the programme that “it wouldn’t have been practical or possible to have made more on the night given the volume of people involved”.
He said: “Rest assured, by the end of today we will be releasing pictures of some of the people we want.
“There will be a huge investigation. I do expect very serious consequences for those involved.”
What started as a non-violent demonstration on Sunday afternoon turned violent after hundreds of protesters descended on the New Bridewell police station.
Two police officers were injured, suffering broken ribs and an arm, and taken to hospital during violent skirmishes with masked thugs.
Later, protesters attempted to smash the windows of the glass-fronted police station.
They also tried to set fire to one of the marked police vans parked outside the station but the small flames were quickly extinguished by riot officers.
Other protesters set fire to a police van parked on Bridewell Street, near to the police station.
Rioters smashed the windows of the police station and also destroyed Avon and Somerset Police vehicles parked nearby, setting fire to a car and a van.
Cars parked in a multi-storey car park adjacent to the police station were also damaged by protesters.
Avon and Somerset Police said its officers had missiles and fireworks thrown at them and used mounted officers and dogs to disperse the mob.
The mindless violence was condemned by the Home Secretary, police federation representatives and local leaders.
Home Secretary Priti Patel tweeted: “Unacceptable scenes in Bristol tonight.
“Thuggery and disorder by a minority will never be tolerated.
“Our police officers put themselves in harm’s way to protect us all.
“My thoughts this evening are with those police officers injured.”
Bristol mayor Marvin Rees said: “I have major concerns about the Bill myself, which is poorly thought out and could impose disproportionate controls on free expression and the right to peaceful protest.
“Smashing buildings in our city centre, vandalising vehicles, attacking our police will do nothing to lessen the likelihood of the Bill going through.
“On the contrary, the lawlessness on show will be used as evidence and promote the need for the Bill."