Fiona, I don't know anything about researching UK vets, but in case no one else offers assistance, I'll try to give you a couple of ideas.
I know that in the case of American vets, it is important to identify his unit down to the lowest level possible. 14th Army was no doubt a very large organization. If you could establish (at least) his regiment (or smaller unit) you would improve your chances. With that info, for instance, you might be able to find a veterans group/association for the unit. Mr. Miller and Mr. Varney may belong to the assn, or the assn might have info on them, or have other members who knew your father.
I'm not sure how to go about getting his service record in the UK, but I would suggest you make an initial inquiry at the UK Nat'l Archives/Public Records Office. Their web address is: http://www.pro.gov.uk/http://www.pro.gov.uk/ Hope someone else can tell you more. Good luck with your search.