A dispersal order to direct people and groups to leave the city centre of Bristol has been issued as demonstrations were held across England against plans to increase police powers.

Despite the Covid-19 lockdown, thousands of people marched in towns and cities in protest against the Police, Crime, Sentencing and Courts Bill, which would give police in England and Wales more 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.

Throughout the day, thousands of people took part in what various police forces described as “peaceful” Kill the Bill protests in regions including London, Newcastle, Birmingham, Liverpool, Dorset and Bristol.

More than 1,000 people attended Bristol’s Kill the Bill protest, according to Avon and Somerset Police, who tweeted early on Sunday a section 35 dispersal order had been issued for the city’s centre following “a number of incidents involving violence between the remaining protesters”.

Earlier, the force said it had reopened the M32 motorway after it was closed to inbound traffic at junction 3 when protesters sat on the road.

By Saturday evening, the Metropolitan Police said that “a small minority” of protesters, who were not social distancing, were still in London’s Parliament Square.

Arrests were being made after they turned down requests to leave, police said.

The Metropolitan Police later said that ten officers had been injured, “none of these are believed to be serious”, and that 26 people had been arrested for a variety of offences including assault on police and breach of the peace.

A woman was arrested on suspicion of possession of an offensive weapon after a knife was recovered.

Commander Ade Adelekan, who described it as a “challenging day for officers”, 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.”

He added: “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.”

Dozens of police with riot helmets had arrived in Westminster as protesters continued the stand-off with officers.

The majority of protesters from the Kill the Bill demonstration, who gathered at Parliament Square earlier in the day, had dispersed several hours earlier.

Those still present shouted “shame on you” repeatedly at officers.

The remaining protesters marched down Whitehall to Trafalgar Square, where violent scuffles broke out with police.

Projectiles were thrown by demonstrators and several people were led away in handcuffs.

Earlier at the demonstration in Parliament Square former Labour leader Jeremy Corbyn told crowds that the policing Bill was a “very dangerous, slippery slope,” as he defended the right to protest.

To cheers and applause, he said: “If we don’t protest, things don’t change.”

But former police minister Sir Mike Penning said the Bill was “not about stopping peaceful demonstrations”.

He told The Sun: “We’ve always cherished our right to protest. But nobody has the right to abuse police officers and bring the country to its knees.”

There was a low-key response from Northumbria Police as hundreds of people gathered beneath Grey’s Monument in Newcastle.

Protesters, including one who held up a placard saying “we will not be silenced”, cheered as a singer with a guitar performed in opposition to the proposed bill.

Demonstrators who marched from the monument through Newcastle city centre chanted: “Whose streets, our streets.”

Many took the knee at the Civic Centre and held a minute’s silence for victims of oppression, after which a round of applause broke out.

Dorset Police thanked those who took part in “peaceful protests” in Bournemouth and Weymouth, and stuck to the Covid-19 restrictions.

Superintendent Richard Bell said: “We have always sought to find the right balance between the rights of protesters and those of residents and businesses, while also considering the very real risks from the spread of the virus.”