One of the arrests was made on suspicion of assaulting a police officer.
Tommy Robinson, the English Defence League founder who now advises Ukip, earlier took to the stage half an hour after the end of the March to Leave rally in Parliament Square to lead a mass sing-along of Rule Britannia.
Tensions between his supporters and the police simmered, with fans of the controversial figure even engaging in a tug of war with officers over metal railings.
Activists chanted “we want our country back” as they then marched on Downing Street.
Tommy Robinson’s supporters have descended on Whitehall’s pubs, with some bringing traffic to a standstill in the capital’s Trafalgar Square, chanting “oh Tommy Robinson”.
A Met Police spokesman said two arrests have been made at the Brexit protests.
“One male was identified as being wanted for an offence in Hertfordshire and subsequently arrested,” the spokesman said.
“One male was arrested on suspicion of assaulting a police officer.
“Both suspects have been taken to a central London police station where they remain in custody.”