The bill’s aim is to apply existing rules for marches to “static” gatherings after protest groups such as Extinction Rebellion were able to bring parts of central London to a standstill.
Sir Peter told Times Radio: “People need to be really worried about this. We’ve learned one thing this weekend, it’s the right to protest, the right to gather, the right to have a voice is fundamental to our democracy, and particularly British democracy.
“Bringing in legislation on the back of the Black Lives Matter and Extinction Rebellion demonstrations, rushing that legislation through, putting in some really dodgy definitions which the police are supposed to make sense of.
“Again if we’ve learned one thing from the coronavirus legislation is that rushed legislation and unclear definitions cause huge confusion for the public and for the police having to enforce it.
“This weekend has shown the crucial importance of the right to protest, and you’ve got to be really wary of more legislation being rushed through just because certain politicians didn’t like certain demonstrations in the summer.”
The Labour Party had previously been expected to abstain but will now vote against the legislation, with shadow justice secretary David Lammy warning that the bill would impose “disproportionate controls on free expression and the right to protest.”
However, the Policing Minister Kit Malthouse accused opposition parties of using the legislation as something to “beat the Government” with.
He said he was “confused” by Labour’s decision to vote against legislation, telling BBC Breakfast: “I’m very disappointed I have to say at the Labour approach and I find it a bit confused.”
Asked about concerns that the legislation will take away the right to peacefully protest, he said it was a “gross exaggeration” and that what they were doing was some “mild streamlining” to put measures on static protests.
Mr Malthouse added: “I think it’s being used a bit to beat the Government in – I hesitate to say – an opportunistic way. It feels like that.”
The SNP and Liberal Democrats were also expected to oppose the bill.