Thousands of campaigners gathered on College Green in Bristol 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.
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.
Avon and Somerset Police issued a warning on Saturday 20 March to anyone thinking of attending the protest.
Insp Rob Cheeseman said: “We’re aware of plans to hold a protest on College Green in Bristol on Sunday 21 March and we’re making efforts to identify the organiser, or organisers, as well as liaising with groups who’ve indicated they are going to attend.
“Under COVID-19 regulations, gatherings are not permitted and pose a real threat of spreading this deadly virus further.
"The communities of Bristol have sacrificed a great deal throughout the pandemic and rates of the virus have been decreasing because of their efforts.
"We all need to play our part and follow the restrictions in place so we can get back to a more normal way of life.
“We don’t want to have to enforce the regulations, but officers will be carrying out enforcement if proportionate and necessary to protect public health."