It is very rare to allocate individual letters to individual pro numbers. That is a nightmare for any filing system - you usually group the activity so correspondence would usually be allocated to the relevant progressive file.
In this case PR 358 would seem to indicate Preston Division 358 with the progressive numbers indicating the activity.
In some cases you could have an identical progressive number if the activity was identical. In my early days on BR, I used to be a tech clerk at various depots and offices on the KX Division and when I was at the AME KX, I had a series of progressive General files for the ODM section (series PG) but also a series of geographically based files for line section and equipment. A good example would be the Northern City Line to Moorgate, part of which we coded P43. The P series suffix letters were then /1 General, /2 Boilers, /3 Lifts, etc.
So P43/3 was Essex Road Lifts but P49/3 would be Letchworth Lifts. Lifts also had a generic file in the PG series. Filing was traditionally on shelves or in metal filing cabinets but I managed to get two hanging file cabinets so the files (in manilla folders) could be easily located and withdrawn. Cross referencing files could be a pain because you might have to copy correspondence but around 1980, the depots got photocopiers!
I always kept file correspondence in reverse date order on the file. At the divisional office we always had a card backing to each file with a star binder inserted (with appropriate card rings top and bottom) to put the correspondence on. I used medium star binders so when the “pad” got too tight I could let another binder on top, interlinking it with the original one. When a pad got too thick, you just created another one, marking it “Pad 2” and keeping Pad 1 handy in case someone wanted it.
Divisional Office KX tended to use shelves, hanging files and filing cabinets. Correspondence files could sometimes be bent in half (with the card side showing, named and numbered) and then kept in wooden tray boxes in a shelve cabinet. I still have the KX Deltic component files in their original two trays, the files being divided into firstly the “owner” in the section (KM2), then the section file reference for Deltics (130) and finally the pro number indicating the subject. So Deltic Horns are in file KM2/130/28.
Each depot, station or office would organise its paperwork differently, according to need or custom and practise. Not everything would be file referenced. Individual staff files in a cabinet would be sorted by name (or section/name), my loco shopping files were organised by loco number and my statutory F88 lifting equipment and tackle registers at the ODM would be organised by geography so that the fitting staff who needed to see them could access them easily.
In the computer age of e-mail and individual correspondence, running a filing system together with all the associated clerical activity now seems like a very long time ago!