The Police, Crime, Sentencing and Courts bill would toughen measures officers can take to disperse demonstrations, such as imposing time and noise limits, which campaigners and activists fear would be used to curb dissent.
Since the bill was brought before parliament last month, there have been sporadic protests, notably in Bristol, southwest England, where demonstrations turned violent with officers and a police station bombarded with bricks and glass bottles, and police vehicles set on fire.
Prime Minister Boris Johnson criticized what he described as "disgraceful attacks" on officers, but protesters have accused police of using heavy-handed tactics.
"As protest is criminalized and our fake democracy is pushed further towards authoritarianism, we seek to find where we can come together with other movements to tackle the common causes that affect us all," said Alanna Byrne from environmental group Extinction Rebellion.
Days of protests by her group paralyzed parts of London in early 2019, action which helped fuel calls from some politicians for the police to be given the tougher powers to prevent excessive disruption.
Demonstrations had not been permitted while a coronavirus lockdown was in place, but restrictions were eased this week, meaning organized rallies can go ahead providing they are "COVID secure."
In London, police warned, "enforcement action will be taken, if needed, in the interests of public health."
Some senior officers have said the "kill the bill" tag was deliberately provocative as "the bill" is a nickname in Britain for the police.