Chief Constable Gavin Stephens, the National Police Chiefs’ Council chairman, said no one was “invisible in a crowd”.
He added: “Officers across the country are looking at intelligence, CCTV footage, body-worn cameras, and will continue to do so. If you are not arrested now, you will be in future.”
A list of more than 30 immigration centres, legal offices and asylum hotels had been shared by far-Right supporters as targets.
Stephen Parkinson, the Director of Public Prosecutions, warned that the very act of sharing the list of potential targets for disorder could come under the scope of terrorism charges.
Mr Parkinson revealed on Wednesday that terror legislation was already being used in one case.
In the City of London, workers were dismissed at lunchtime amid fears that disorder could prevent them from getting home safely at the end of the working day.
One office worker in a City firm said he and his colleagues had been told to leave their office near Liverpool Street because of “planned riots” in the area, and would work from home for the rest of the week.
In Middlesbrough, the scene of widespread disorder at the weekend, many businesses closed early, with some boarding up windows.
A Cleveland Police spokesman attempted to reassure the local community, saying: “The force is resourced and well-equipped to manage any additional disorder, and we will be using all powers that are available to us to help us prevent disorder.”
The ongoing disorder is thought to be having a major impact on businesses in the areas worst affected. The Federation of Small Businesses (FSB) said it was doing what it could to help small firms worried about being caught up in the unrest.
Martin McTague, the FSB national chairman, said: “Millions of small businesses are on our high streets and town centres, populating our local communities and finding themselves on the front line of the recent public disorder, violence and damage which all come at human cost.
“Local authorities, insurance companies and politicians of all stripes need to be ready to support their small businesses to rebuild, recover and get back on their feet.”
By 7pm on Wednesday, hundreds of counter-protesters had gathered at sites across the country.
In Walthamstow, a crowd amassed carrying banners reading “Oppose Tommy Robinson” and “Refugees Welcome” amid fears that far-Right agitators were planning to target an immigration lawyers’ office in the town centre.
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