Could be Dawes, they and Elswick were the main suppliers, before Pashley got the contract, certainly remember them when I started on the Post,
I had a double top tube on my Dawes posty bike, coz I was a big leggy ( still am ) back then.
Looking at the front rack, I'm guessing it's a Pashley, the Dawes had a mesh platform with long leather straps, the Pashley came with a basket affair and a plastic tray insert.
I doubt a frame no. will be of any help, that was a Royal mail identifier.
Incidentally, posties got an allowance for basic maintenance and cleaning, Paraffin was issued to clean the bike, anything more than oiling and brake adjustment, was done by the likes of me,who had an interest in bikes ,as part of the office duties, a full strip down and inspection every 3 months, and if deemed condemned, we had to cut the seat stay lugs out, coz that's where the frame no. was, then give it to the 'Guvnor.