Officers were called to Cheddar Gorge on Thursday 9 April following reports of several vehicles being driven dangerously.
One motorist was stopped after trying to make off from officers.
The male driver was reported for allegedly driving without tax, driving without due care and attention and not maintaining the car to a safe standard due to insufficient tyre tread.
The driver had previously been warned regarding antisocial driving and following this latest incident the vehicle was seized.
The vehicle was searched and the 29-year-old male was arrested on suspicion of driving under the influence of a class B drug and possession of class B drug. He has been released under investigation.
Enquiries are being carried out to try to identify other vehicles involved, one of which is believed to be a red BMW 3 Series.
PC James Fowler said: “We take reports of antisocial behaviour and driving in Cheddar Gorge extremely seriously, no more so now than when we are all being asked to stay at home to protect the NHS and save lives.
“We will continue to patrol the Gorge to try to prevent a repeat of this antisocial behaviour.
“If anyone can help us identify the other drivers involved, please contact us.”
Anyone with information can report it online and give reference number 5220079552. Alternatively, if you cannot report it online, call 101.