It is a No.4 Mk1 that was upgraded to No.4 Mk2 specifications and re-designated a No.4 Mk1/2. The (F) is for the Fazakerley factory where the Factory Through Repair (FTR, basicaly a rebuild) was carried out. (as mentioned above)
Its definitely British made, look on the left side of the but stock socket. Their should be a production code.
I believe The "BNP" you noticed stands for "British Nitro Prof", its a commercial marking that was added when the rifle was sold off. All rifles in British public hands were/are required to have it. Their should also be something along the lines of " .303 2.222"" and "19.5 tonnes per []"" as well.
For clean up, Not a whole lot you should do. If you want you could remove the stock set and give the metal a good scrub if needed. Just use a toothbrush, a rag, and some good oil. for the wood, the standard maintenance involved routine coats of linseed oil to keep the stock "hydrated" with oil. You could do that but be very gentle around the rack number so you don't accidentally remove them with the linseed oil. But it looks quite alright.
Quite surprised it was found in a C can Its in very good shape. Very nice find, should make an excellent shooter.
