The protest in London on Saturday was held outside of the Thistle City Barbican Hotel in Islington, with a counter-protest led by the group Stand Up To Racism.
The Met said the protest was organised by local residents under the banner “Thistle Barbican needs to go – locals say no”.
But police said it had been “endorsed by groups from outside the local community which is likely to increase the number of people attending”.
The MP for Islington North, former Labour Party leader Jeremy Corbyn had urged people to join the counter-protest.
The police had imposed special restrictions ahead of the London demonstration, including setting out specific areas where each group had to remain.
In Newcastle, a protest and counter-protest took place outside The New Bridge Hotel.
Four people were arrested and remain in custody, according to Northumbria Police.
“The right to lawful protest is a key part of any democracy, which the police uphold,” a spokesperson for the force said.
“However, we will not accept people using them as a means to commit crime or disorder.”
About 1,500 people waved England and Union flags in a march organised by the Britain First group from Manchester Piccadilly rail station to outside the Central Library, where they held a rally.
About 250 people were also estimated to be at a counter-demonstration led by the Stand up to Racism organisation, with police keeping the groups apart in St Peter’s Square.
Greater Manchester Police said that a “number of demonstrations passed by peacefully” with “no incidents of note”.
But two arrests were made during a confrontation at the start of the march, the statement added.
One person was arrested for theft and the other for obstructing an arrest.