Residents living close to the Central car park have been complaining for years about drivers and other groups congregating their in the evenings and after dark.
CCTV cameras have been put in place and other measures taken to try and deal with the problem.
In a motion to Wednesday night's town council meeting, Councillor Duncan Kerr has called for a request to go into Shropshire Council to make a Public Space Protection Order.
He says: "Whilst the council is appreciative of the actions of the police to try and resolve the disturbance being caused by the anti-social driving of motor vehicles on Central Car Park, it is apparent problems have not yet been eliminated.
"I ask that, in recognition of the severity of the situation, the council formally requests Shropshire Unitary Council to seek a Public Space Protection Order under the Anti-social Behaviour, Crime and Policing Act 2014, which would then prohibit this activity and increase enforcement powers."
He said that such action had been successfully used by many other councils.
Residents say drivers come into the town to use the open space often doing laps on residential streets, as well as playing loud music on the car park and revving their car engines.
Central car park currently has 24-hour access.