Police said the alleged offences took place around 19:50 yesterday evening (Sunday 24 July).
In an appeal for witnesses, officers reported: “A Silver Mercedes-Benz CLK 320 travelling East-Bound on Victoria Avenue, near to the lower park, has failed to stop for a police officer during a speed check and continued in the general direction of the Grand Hotel.
“A male in his 20s was subsequently arrested at his home address.”
In particular, the Force would like to hear from anyone who was in the queue of traffic and saw the driver, particularly his manner of driving, and a man and woman who spoke to the officer conducting the speed checks immediately after the incident.
Anyone who may be able to help is asked to call 612612 or make an anonymous report via Crimestoppers on 0800 555111 or their online form.