Sand and water were thrown as police attempted to keep apart two rival groups of protesters in a seaside town.
Officers had formed a line on the beach in Cleethorpes, North East Lincolnshire, where hundreds of anti-racism and counter-protesters gathered.
Though the event was "largely peaceful", police said a "small group" not involved with Black Lives Matter threatened and assaulted officers.
Two people were arrested on suspicion of assaulting a police officer.
They remain in custody, Humberside Police said.
Crowds gathered at the seaside town's leisure centre before heading to the pier for a rally.
Veterans and others had surrounded a seafront war memorial over concerns the site may be defaced.
MP for Cleethorpes Martin Vickers said racism "must be stamped out". He urged visitors to stay away and others to observe social distancing.
Protester Janine said: "We just want people to understand that injustices need to be dealt with properly."
Protests in England
Fellow campaigner Mustafa Ali said: "It's not easy when you get called racial words and abusive things or when you go to a football game and you just want to enjoy your time."
Veteran Tony Dugard said: "There's a good veteran turnout but there's also a large turnout from the community that we have no control over unfortunately."
Mr Dugard said he had hoped the protest would "go peacefully".