Hundreds of campaigners have gathered in Lemon Quay in Truro to protest the Police, Crime and Sentencing Bill.
The bill would change how protests are policed and making some aspects of the Coronavirus Act permanent.
Currently, police have to show a protest may result in “serious public disorder, serious damage to property or serious disruption to the life of the community” before they are able to put restrictions on it.
They also need to prove protesters know they’ve been told to move on.
The new bill would mean permission for protests needs to be granted in advance and protesters could be fined £2,500 if they go ahead with a protest without permission.
Protest organiser and civil liberties campaigner Emily said: "So many of the rights that we take for granted have been won by disruptive protest and so criminalising this further is a real attack on our fundamental rights that we have in this country.
"But the Government doesn't seem to care about that, they seem to just want to be able to really try and scare and intimidate people off the streets.
"It's really interesting coming here today with the Covid regulations because none of us want to be out on the streets with Covid, we've all been very strict about not being out but we have to question what kind of world we're going to end up in when this is over and this fight has to happen now or it'll be too late.
"We don't want to be here but we have to be here because we have to say that this bill cannot go through because it is such a fundamental attack on our civil liberties."
Similar protests are being held across the country this week, with campaigners claiming that the new bill undermines their right to peaceful protest.