I think the Dorchester referred to is Dorchester on Thames (Oxfordshire? - may have been Berkshire then) rather than Dorchester, Dorset (or Dorchester, Ontario....).
I'm sure I've seen a reference by somebody to calling in (on the way from Silverstone?) to check on Piper who was doing an "all nighter" on that car.
Yes, probably Dorchester-on-Thames. Phone book records between 1959 and 1963 give the address as just 'Oxford Road', which is today a cul-de-sac leading to an old gravel pit. No obvious former garage premises, but most of the houses look 1960s or later.
However, there was also a Dorchester Service Station in Dorchester, Dorset. And both are in the 1961 phone book.
There was another in Dorchester Rd, Hazel Grove, Manchester, but not until later in the 1960s.
Robert Bodle (Banbury) Ltd seems to have been a car dealer. Address in 1961 is Continental Car Centre, 57 Parson's St, Banbury. Looks to now be a pedestrianised area, as it's not on Google Street View. Company was wound up in 1968.