Pro-Brexit activist James Goddard has been arrested in connection with incidents outside Parliament on Monday.
Police said a man in his 30s was arrested outside St James’s Park Tube station in London just before midday.
He is being held on suspicion of a public order offence.
Mr Goddard was involved in a protest in Westminster earlier this week during which Remain-supporting Conservative MP Anna Soubry was called a Nazi.
A Met Police spokesman said the arrested man was currently in police custody and being taken to a central London police station.
BBC home affairs correspondent Daniel Sandford said Mr Goddard’s supporters said he had been about to hand himself in at a London police station.
His “small” group of supporters were angry about his arrest, our correspondent said.
In recent weeks, an increasing number of protesters have gathered opposite the House of Commons, shouting and waving flags about Brexit as broadcasters interview MPs.
The BBC and other broadcasters have set up temporary studios on College Green, a traditional spot for political interviews, ahead of the Commons vote on Theresa May’s Brexit deal on 15 January.
On Monday, Conservative MP Anna Soubry was called a “Nazi” by protesters during a live BBC News interview.
Earlier that day, she had faced barracking by a group of protesters as she walked to Parliament.
In the wake of the incidents, Ms Soubry, who supports another Brexit referendum, criticised the police for not intervening at the time.