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The council is being urged to get tough with boy racers by introducing new punishments, including £1,000 fines.
People in the Towns were asked to take part in a consultation regarding so-called public space protection orders (PSPO).
The results showed 93% of the 931 respondents wanted anti-social behaviour in cars to be dealt with as a priority.
Now a report going before Medway’s Cabinet next week, recommends a Towns-wide PSPO be approved to introduce fixed-penalty notices and prosecution for those who cause public nuisance in their cars.
The consultation asked about problems, including racing, stunts, revving engines, excessive noise, speeding, burnouts and whether action was needed to clamp down.
Car cruising - where drivers meet on public roads to race or show off their vehicles, often driving slowly and taking up all lanes - was also raised as a major concern.
If brought in, the PSPO would give the police greater powers to stop offenders, issue fines, or even seize their vehicles.
Based upon other areas where orders have been introduced, officers could hand out on-the-spot fines of £100 while serious breaches could result in prosecution leading to a maximum fine of £1,000.
The consultation was held between February and May, with 85% of respondents saying they had experienced vehicle behaviours that had caused excessive noise, nuisance, annoyance, danger, or risk of harm.
Residents were also asked what time these problems tend to occur, with the greatest number saying the offences happen between 7pm and 11pm on Fridays, Saturdays or Sundays.
The report says the expansion of police powers to crack down on these behaviours would come at no extra cost, and any additional associated signage would be paid for out of existing budgets. If approved by the Cabinet, it will go to the next full council meeting on October 19.
The local authority could not give a firm date of when the PSPO would come into force if approved.
The report said over the past 18 months, Medway has seen a dramatic increase in complaints related to anti-social behaviour in cars and the level of response to the consultation seems to corroborate this.
At a Home Office oral questions session, Rochester and Strood MP, Kelly Tollhurst (Con), asked if the funding for Kent Police could be looked at due to increased pressure from the kind of behaviour that the PSPO is trying to tackle.
Policing minister Chris Philp said the police funding formula would be looked at and urged Medway Council to implement the PSPO.
The issue has been raised consistently by residents and business owners saying it keeps them awake late at night and attracts other problems like vandalism.