Born in West Bromwich, Staffordshire, Ashmore came from a racing family, his garage-owning father Joe and uncle Fred having raced private Maseratis in partnership with Reg Parnell immediately after the war.
Gerry cut his teeth on Jaguars before, along with his brother Chris, racing in Formula Junior in 1960. Later that summer he traveled to Europe and raced at Zeltweg and Innsbruck, finishing third behind Hans Herrmann and Wolfgang von Trips.
In 1961 he raced a Reg Parnell Lotus 18 and later with The Three Musketeers (André Pilette, Tim Parnell and Gerry Ashmore). He was due to appear in the Lombank Trophy on the 26 March at Snetterton, but the car had not been delivered so he had to wait until the Großer Preis von Wien on the 16th of April at the Aspern Aerodrome to first race the car. He was thrid fastest in qualifying behing Moss and Shane Summers. Unfirtunately he went out on the 5th lap of 55 with brake problems. Back in England for the Aintree 200 the following week he finally finished all be it two laps down on the winner, Jack Brabham
In May he drove at Posillipo in the XIV Gran Premio di Napoli. Ashmore qualified on pole in front of Salvadori and Giancarlo. Baghetti took the lead on lap 4, with Salvadori in hot pursuit. Roy picked up a puncture on on lap 26, while Ashmore had dropped back and was now out of touch with Baghetti. Baghetti spun on lap 53 and even though Ashmore unlapped himself, he was not in a position to catch the Ferrari. Baghetti went on to take the win with Ashmore in second.
In the summer he took part in the British GP with a privately-entered Lotus but retired after a few laps.
Later in the year he traveled to Europe again to race at the German and Italian GPs but without success, his Monza outing ending on the first lap in a big accident independent from the von Trips tragedy. He was due to race in the Lewis-Evans Trophy at Brands Hatch in October but neither the car or Gerry had recovered form the Monza incident.
After a handful of races with the Lotus in 1962, he continued to make occasional appearances, such as in 1965 with the ex-David Prophet Lotus 30 and in 1970 driving a Lotus Elan 2+2.
Now retired and living in France. He is still a regular visitor to historic festivals and reunions.