...my thoughts are - if a private individual/small group were able to introduce OHL▸ on a shoestring (presumably) for this tramway why cannot Network Rail electrify branchlines at reasonable cost?
I am expecting a whole load of reasons from forum members more knowledgeable than I am.
I believe that branch lines could be electrified at much lower cost than at present. New conductor rail installations are de facto banned.
A cheaper possibility would be
OHLE▸ at 750 volts
DC▸ . Already used for trams so the equipment is at least somewhat standard.
DC electric trains are a mature and well understood technology, and the train need not "know" that the current is from an overhead wire and not a live rail.
The move away from all 25 KV
AC▸ would be regrettable, but arguably a price worth paying for cheaper, simpler, and less obtrusive electrification of branch lines. Performance would be limited to keep down the current and the related costs, but remember we are talking of branch lines, not intercity.
A class 159 has reasonable performance with a power of about 900 kw, something similar but electrically powered is probably about the sensible limit with 750 volt DC overhead.