The Metropolitan Police said several protests are scheduled in the capital on Saturday, including a Black Lives Matter demonstration.
Measures including requiring the events to end at 17:00 BST are in place following violent scenes last weekend.
But the police force warned protesters to reconsider attending at all due to the coronavirus pandemic.
“We are asking you not to come to London, and let your voices be heard in other ways,” Met Commander Bas Javid said.
The restrictions come in the wake of violence and serious disorder in Westminster at the end of protests last weekend.
The new conditions, set out on the Met’s website, apply to Black Lives Matter, and to left and right-wing groups that have notified the force of their intention to demonstrate on Saturday.
Restrictions mean Black Lives Matter demonstrators must stick to a specific route between Hyde Park and Trafalgar Square, where they will be permitted to assemble until 17:00.
Similar regulations applied to right-wing groups require them to assemble in Parliament Square and some parts of Whitehall, again until 17:00.
The Met said police officers routinely talk to organisers before and during an event to minimise disruption and disorder.
“Policing demonstrations is complex and challenging, not least during a global health crisis,” Commander Javid added.
“We will continue to police any protests with the aim of keeping people safe and preventing crime and disorder.”
Denise Richards, who is involved in the Black Lives Matter movement in Derbyshire, said her chapter had decided not to protest in London on Saturday, and she believed other groups across the UK felt similarly.
She told BBC Radio 4’s Today programme that peaceful protesters feared they would be caught up in violent clashes with far-right demonstrators and this could “tarnish” the work of Black Lives Matter.
However, she said smaller protests would still be taking place in towns across the UK.
Nick Lowles, chief executive of campaign group Hope Not Hate, said there was a “very serious” threat of trouble from far-right activists and commended Black Lives Matter for standing down their plans to protest in London on Saturday.
“There are some people who are genuinely concerned about the protection of their statues and monuments but many people are coming for a fight and they are talking openly about it on their social media accounts,” he told the programme.
A Black Lives Matter demonstration took place in central London on Friday evening with leaders of the march urging those in attendance to keep the demonstration “peaceful” and not to join any anti-racism rallies planned for the weekend.
Hundreds of campaigners surrounded Nelson’s Column in Trafalgar Square after walking from Hyde Park, as around two dozen police officers watched on.
‘Absurd and shameful’
Earlier, a statue of war-time leader Winston Churchill in Parliament Square was boarded up to protect it from potential damage.
The move was branded “absurd and shameful” by Prime Minister Boris Johnson.
Mr Johnson said the former prime minister had expressed opinions which were “unacceptable to us today” but remained a hero for saving the country from “fascist and racist tyranny”.
Protesters daubed “was a racist” on Churchill’s statue last weekend.
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In a series of tweets, Mr Johnson urged people to “stay away” from demonstrations amid the coronavirus pandemic.
“We cannot try to edit or censor our past,” he wrote of moves to remove tributes to historical figures. “We cannot pretend to have a different history.”
Other monuments have been removed ahead of separate protests planned over the weekend, while the Cenotaph war memorial, in Whitehall, has also been covered.
In Poole, Dorset, a statue of Scouts movement founder Robert Baden-Powell is to be cladded instead of removed.
Mayor of London Sadiq Khan said other “key statues”, including one of Nelson Mandela, would be protected.
It comes after the statue of slave trader Edward Colston was thrown into the river in Bristol during a Black Lives Matter protest on Sunday.
Demonstrations have been taking place across the world following the death in police custody of George Floyd in Minneapolis last month.
Mr Johnson said that, while he understood “legitimate feelings of outrage” at Mr Floyd’s death, the “only responsible course of action” was to “stay away from these protests”.
The prime minister said the demonstrations had been “hijacked by extremists intent on violence”.
He added that whatever people’s feelings about the cause they should not support a demonstration which “in all probability” would “end in deliberate and calculated violence”.