Three quarters of people responding to a survey in Bury St Edmunds said they had been affected by anti-social behaviour from boy racers in the town, latest figures show.
It would also curb foul or abusive language from drivers, threatening or intimidating behaviour towards people or causing obstructions in the road.
It is understood the problem is largely in relation to gatherings in car parks and the town centre.
If approved, the measures would be an extension of an existing public space protection order (PSPO) – an order which imposes tougher sanctions on issues like alcohol-related anti-social behaviour and street begging.
If any of those conditions were breached, it would be considered a criminal offence.
Acting Inspector Sonia Plume said: “Suffolk Constabulary is supporting St Edmundsbury Borough Council regarding an amendment to the existing public spaces protection order in Bury St Edmunds.
“This is after issues were raised by the public and local residents regarding an increase in the nuisance of anti-social behaviour related to the use of vehicles in the town centre.
“This activity can clearly have a detrimental impact on the quality of life for those in the locality.
“Having a PSPO in place will allow authorised council officers as well as police officers and PCSOs to take appropriate enforcement action against those involved.”
A public consultation on the plans was held over four weeks in January and February, where 75% of 32 respondents said they had been affected by anti-social behaviour caused by the congregation of vehicles in the town.
A report prepared for January’s scrutiny committee debate on the subject said attempts to engage with the gatherings had resulted in short term improvements but new people each year meant the problems started again.
Councillor Robert Everitt, cabinet member for families and communities at St Edmundsbury Borough Council said: “We have been listening to and working with the local community and police to find the best way to crack down on this type of anti-social behaviour.
“If agreed by joint cabinet this will further enable the police with our support to take decisive and effective action on this problem which is a concern for residents and businesses alike.”
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