Video report by ITV News Correspondent Mark McQuillan
Police have made 26 arrests at London's Kill the Bill protest, while 10 officers have been left with injuries not thought to be serious.
The Metropolitan Police said arrests had been made "for a variety of offences" including assault on police and breach of the peace.
The force said one woman was arrested on suspicion of possession of an offensive weapon after a knife was recovered.
Scuffles broke out between officers and protesters outside Parliament, projectiles were thrown as police pushed demonstrators away and at least one officer was injured.
Thousands took part in largely peaceful protests across the country on Saturday, voicing their opposition to the government's proposed policing bill.
Dozens of police with riot helmets arrived in Westminster shortly afterwards as those at the march continued to stand off with officers. Protesters booed police and chanted "shame on you" at officers.
The London protest was one of many taking place around the country on Saturday.
London, Bristol, Newcastle, Cardiff, and Manchester were among the cities that saw action, with other marches held on Friday.
The controversial policing bill would give police power to impose conditions on non-violent protests, including those deemed too noisy or a nuisance, with those convicted liable to fines or jail terms.
ITV News Correspondent Martha Fairlie has more from the situation in Bristol
Events were largely peaceful throughout the day.
A Kill the Bill protest in Bristol last month turned violent, with clashes between police and protesters.
Around 5,000 people gathered again in Bristol on Saturday, for the fifth Kill the Bill demonstration in the city centre in the past two weeks.
Protesters briefly held up traffic on the M32 motorway in the city on Saturday night.
Police were forced to close the road but was cleared and reopened within 30 minutes.
In the latest easing of lockdown restrictions in England, protests are now lawful once again - providing organisers submit a risk assessment and take steps to ensure the gatherings are safe.
Former Labour leader Jeremy Corbyn spoke to the crowds in London.
In a tweet he posted ahead of the demonstration he said the right to fight injustices and to give “a voice to those often unheard” is “once again under threat from a dangerous bill which effectively criminalises peaceful protest”.
He said: “The right to protest is precious.
“Protest movements make history, from the eight-hour working day to the vote for women to the right for equal pay, the rights we take for granted had to be won through protest.
“We took them – they weren’t handed to us by the rich and powerful.”
Commander Ade Adelekan, who led the Metropolitan Police's operation, said: “The vast majority of people who turned out in central London today did so while adhering to social distancing. They engaged with my officers when required and left when asked – I would like to thank them for doing so.“However, a small minority did not engage despite the repeated efforts of officers on the ground. This left us with no option but to move to an enforcement stage and arrests have been made.“This has been another challenging day for officers on the ground and I want to thank them for their efforts throughout the course of today.“We remain in the middle of a global pandemic and we have made great progress in controlling the spread of the virus; we will not allow the selfish actions of a small number of people to put Londoners progress in jeopardy.”
In Newcastle several hundred people gathered beneath Grey’s Monument before marching through the city centre.
At the Civic Centre many took the knee and held a minute’s silence for victims of oppression, after which a round of applause broke out.
There was a low-key response to the city centre gathering from Northumbria Police.
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