You've got it pretty well, in one. The U is the Country, such as United Kingdon or B for Belgium on our L9 pistols. E is Enfield, F, Fazakerley, P Parker Hale. A Accuracy International, S Sterling and so on. The year prefix then A-. followed by the sequential serial number of usually 5 numbers. BUT, there is some dispute about the numbers because when BSA took over the Fazakerley contract, because they had already commenced certain serially numbered components, suc h as triggermechanism housings and some bodies, identifed with a flat top across the carrying handle nut area(?) those numbers allocated to Fazakerley L1A1's were prefixed with an additional 1 at BSA. So you COULD get UB58A121585, the first figure 1 indicating that it was a Fazakerley body.
I had this as an L1A1 number and it's been questioned but there are others like this so............ This will get some going as it doesn't seem to be recorded anywhere but this was told to me by Major Chris xxxx, the person who used to allocate serial numbers!
Numbers were allocated to production. So if Parker Hale were contracted to supply 1000 L81A1 rifles, they'd be allocated serial numbers UP 80 A0001 to UP80A 1000. That's a general rule.................