Scaffolding was filmed being put up around the statue and the nearby Cenotaph on Thursday evening.
It came amid fears of clashes on Saturday between right-wing groups, who vowed to “defend” selected memorials, and Black Lives Matter demonstrators.
A spokesperson for the Mayor of London said: “The statue of Winston Churchill in Parliament Square is being temporarily covered for its protection.
“The overwhelming majority of protests have been peaceful, but after recent damage the decision was taken by the Greater London Authority City Operations Unit to cover it.“
The wartime prime minister’s figure was targeted with graffiti during a march last weekend, while a demonstrator tried to set a union flag on the Cenotaph alight.
The statue of anti-apartheid revolutionary Mandela was also put under a protective covering after far-right group Britain First called for it to be “torn down”.
Several statues of historical figures linked to the slave trade, colonialism and racism are facing calls for removal.
Police fear that demonstrators will attempt to vandalise or remove controversial memorials following last week’s toppling of the statue of 17th century slave trader Edward Colston in Bristol.
Martin Hewitt, chair of the National Police Chiefs’ Council (NPCC) said it had “created a wave of activity”.
“It’s not a matter for police unless a criminal offence has been committed, it’s a matter for the guardians of the statues dealing with those people who feel very strongly,” he told a remote press conference on Thursday.
“That’s how it should go forward … it should be done peacefully and it shouldn’t be dealt with by criminal acts.”
Chief Constable Ben-Julian Harrington, the NPCC lead for public disorder, said police leaders across England and Wales were working with the authorities responsible for statues and memorials that could be targeted to put “appropriate plans in place”.
If protesters try to take down more statues, Mr Harrington said local police commanders would make decisions on whether to intervene depending on the circumstances.
“I’m not saying officers will or won’t protect statues, it will depend what they see and the threat to the public and property,” he added.
“They will protect property but people come first, so I can’t describe what they will or won’t do.”
Mr Hewitt said that anyone vandalising or tearing down statues would still be investigated and “dealt with”.
On Thursday evening, a Bristol tower block sign bearing Colston’s name of a slave trader was removed.
Guy's and St Thomas' hospitals in London announced it will remove two statues of their namesakes from public view due to their links to the slave trade.
Bournemouth, Christchurch and Poole Council have delayed plans to temporarily remove a statue of Scouts founder Robert Baden-Powell after angry residents vowed to fight to protect it.
The council had originally said it would move the statue from Poole Quay on Thursday over concerns it was on a target list compiled by anti-racism activists.
Campaigners have focused on Lord Baden-Powell due to his associations with the Nazis and the Hitler Youth programme, as well as his actions in the military.
The statue features on a “topple the racists” website which lists more than 60 statues and memorials across the UK which they argue should be taken down, because they “celebrate slavery and racism”.
In a statement issued on Thursday afternoon, the council said the listing “placed the much-loved statue at risk of damage or even destruction”.
The council said the statue would not be removed because its “foundations are deeper than originally envisaged” with discussions needed with contractors on how to move it safely.
Twenty-four-hour security will be put in place “until it is either removed or the threat diminishes”, the council said.
Since George Floyd’s death in Minnesota on 25 May, police have recorded 199 protests across the UK attended by an estimated 155,000 people.
As of Wednesday, there had been 137 arrests and over 60 police officers injured.
The Metropolitan Police Federation, which represents rank-and-file officers in the capital, condemned the violence.
Chairman Ken Marsh told The Independent protests would be “policed differently” in London this weekend.
But he said officers had “massive concerns” about a potential influx of football hooligans and Tommy Robinson supporters into the capital.
The Democratic Football Lads’ Alliance, which claims to oppose extremism but has been linked to far-right elements, called for supporters to gather in Whitehall on Saturday and Robinson urged all “patriots” to attend.
“There is concern because there are large groups coming to London who will clash with each other, and it will be our job to stop that happening,” Mr Marsh said.
“I think officers will do their utmost to stop criminal damage happening.”
He said that protests so far had been mostly peaceful and that “99.9 per cent of the people who attend have no intention of committing violence”.
Black Lives Matter London said a planned protest in Hyde Park on Saturday was cancelled, although a similar event on Friday will still go ahead.
“We want the protests to be a safe space for people to attend however we don't think it'll be possible with people like them present,” an Instagram post said.
Large protests are illegal under coronavirus lockdown laws, which still ban public gatherings of more than six people.
The prime minister's official spokesman said that while Boris Johnson understood the strength of feeling on the issue, rules were in place to prevent the spread of Covid-19.
“He has been very clear that any gatherings of more than six people would be illegal and would urge people not to take part in protests if they can't be conducted in a lawful way,” the spokesman said.
“If people aren't able to follow the rules - and any protests are therefore unlawful - he would strongly urge people not to take part.”
But police leaders said they had no plans to shut protests down or tell organisers to call them off.
“We don’t tell people not to protest because it’s an important right,” Mr Harrington said. “We are advising them that a group of more than six is against the law.”
Mr Hewitt said officers were balancing the “competing demands” of the coronavirus outbreak, Health Protection Regulations and right to protest.
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