Happy to! Although I’m a bit late to the thread.
All sort codes do technically still relate to a “branch” in the system, in the sense that they all relate to a branch address. However, as far as I’m aware, Nationwide has never (and when I say never, I mean during my lifetime) used branch-based sort codes, they are all centrally allocated. This is the same as a branch-allocated sort code, except that the associated address is their Head Office in Swindon.
These days, since all banking processes actually take place on a banking mainframe backend, and credit lending is based almost entirely off algorithmic analysis of your account and personal data, it doesn’t matter if you attend your “home” branch or any other. A branch is simply another “channel” for interacting with the customers, like internet or phone, and nothing more than that. In the good old days, as others have said, your allocated branch would have been the home of your account and decisions would have been made locally at that branch - and your account would have been directly managed by that branch. Handelsbanken still have this approach, and so do select private banks like C Hoare & Co or Coutts. Mass market banks don’t, however.
Fintechs usually only use one sort code, which relates to the central office in the same style as Nationwide. Other traditional banks like RBS do still have “local” sort codes, but they don’t mean anything.
It is possible to transfer sort code, but you would also need a new account number as account numbers are allocated per sort code - so to simply port it across would potentially create a clash with another customer at the new sort code. I imagine that RBS were talking about a backend process which effectively would have “renunbered” your account so it came under Holts. You are also right that Holts is both Holts Military Banking and RBS Farnborough in the same building. Child & Co is the same - there is a sort code for RBS Fleet Street which creates bog standard customer cards and chequebooks.
If you are interested to see the address mapping of your “branch” you can always type a sort code into the Faster Payments Checker. It doesn’t tell you the full address, but does give the linked branch details.
I believe that Holts customers can also use any NatWest or RBS branch for basic cash or cheque transactions, but advice on specialised Holts products would have to be at the Farnborough branch or over the phone. However, I don’t believe you actually ever have to attend the branch in Farnborough unless you want to. You can speak to your relationship manager over the phone, and it doesn’t matter where they are.