Senior officers admit they lost their grip on the chaos that engulfed the Whetley area of Bradford.
But they insist the local force has a great record in tracking down miscreants in the cold light of day.
And Assistant Chief Constable Greg Wilkinson had a stark message for the troublemakers.
He said: "We have an excellent record in follow-up arrests. These people who have been involved had better keep looking behind them."
ACC Wilkinson said his officers had displayed "ultimate courage and bravery", adding that he was "very annoyed" at what they'd had to put up with.
Defending the police operation, he said it was not true that police had "allowed" the riot to take place.
He said: "When you are faced with a rioting mob of five to seven hundred people you can't just click your fingers to stop it.
"Perhaps I had underestimated the threat. Obviously tension had risen because of the National Front wanting to have a demonstration.
"There was certainly a growing feeling that said Bradford did not want to be dictated to by outsiders. But the ferocity and seriousness took everyone by surprise."
Asked if the police lost control, ACC Wilkinson said: "There were times when we didn't feel completely on top of the situation and were extremely stretched. Officers had been out there for 12 hours. Many, in full riot gear in the heat of the afternoon, were exhausted by the time the main confrontation began.
He said the police strategy had been to "contain and disperse" the rioters - it had clearly failed, because of the damage caused.
ACC Wilkinson estimated between 12 and 20 right-wing extremists were in town. "They made their presence felt and dispersed early," he said. "They were very important - they were a catalyst."
Officers revealed five known National Front members were met, mid-afternoon on Saturday, by police at Bradford Interchange and turned away from the city.
ACC Wilkinson said it was wrong to categorise the rioting as 'race riots', saying: "Criminality is more of a motive than race."
There was no toughening-up for Sunday compared to Saturday, but officers were fresh and a "significant number" of officers were available last night. There were "far more resources", he said.
ACC Wilkinson said other tactics - including the use of plastic bullets - were available to police. But he said: "You'd be looking at loss of life before you'd commit to using those."
West Yorkshire police does not have a water cannon - used in other places to control rioting crowds. ACC Wilkinson added: "My wife thinks one of those would be a very good idea."
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