I think you may be right @re, although I cannot find out what the exact differences are between the Cox and the Heerey, I did however find this piece of info -
The GTM marque was launched in 1967 when Cheshire garage owner Bernard Cox and a friend Jack Hosker created the Cox GTM (Grand Touring Mini). The car was mid-engined and the fibreglass bodywork contained more than a hint of Ferrari Dino in its styling.
The Cox GTM's unveiling at the January 1967 Racing Car show created great interest and a small group of staff began to assemble kits as fast as they could in Bernard Cox’s garage in Hazel Grove.
Howard Heerey, who had helped Jack Hosker with the styling of the car, raced the road registered prototype during the 1967 season achieving several class placings. For the 1968 season, Heerey raced a specially built lightweight GTM racer, however by the autumn of 1968, Bernard Cox had decided to cease production and it is believed that just over fifty kits had been produced by the Cox garage.
Having raced the Cox GTM the young Howard Heerey knew the car’s potential and in February 1969 Howard and his father (who ran the Midland garage, located only 100 yards from the Cox garage) took over the project and the car was renamed the GTM. Heerey continued to improve the design and in early 1971, after some 170 cars had been built by the company (now known as Howard Heerey Engineering Ltd.), the Heerey GTM 1-3 was announced (model 1, variation 3).
The 'G' registration was issued between 01 August 1968 and 31 July 1969. so based on that it's either an early Heerey or a late Cox, not much help really!