People joining the Black Lives Matter demonstrations on Saturday must be off the streets by 5pm, according to conditions laid down by the Metropolitan police.
Protesters have also been told that they must stick to the planned route, from Hyde Park to Whitehall.
The force fear the anti-racism protests – that were sparked by the death of George Floyd in the US last month – could be met with counter-demonstrations by far-right groups.
The 46-year-old African American died after a police officer held him down by pressing a knee into his neck in Minneapolis on 25 May, provoking riots in many US cities and demonstrations across the world.
On Saturday, those affiliated to the Black Lives Matter protests must remain north of a police barrier erected on Whitehall, while far-right protesters must remain to the south of the line. The conditions were set under section 12 of the Public Order Act.
Organisers of one demonstration planned for Saturday cancelled the event over fears of conflict with far-right protesters, but the Met thinks thousands will still attend.
On Friday, statues in Parliament Square including Winston Churchill, Nelson Mandela and Mahatma Gandhi were boarded up to prevent them being targeted by either side.
Met commander Bas Javid, brother of former chancellor Sajid, said he understood the depth of feeling of protesters, but asked people not to come to London while lockdown rules were still in force.
“If you were planning to come to London, I again would urge you to reconsider, but if you are still intent, please familiarise yourself with what the conditions are,” he said. “Please keep yourself safe by complying with government guidance on social distancing.”
Anti-racism group Hope Not Hate has said football gangs from West Ham, Chelsea, Millwall, Sheffield Wednesday, Hull and Spurs were among the groups planning to come to London.
Far-right group Britain First has also said its members will attend.