The record books of the firearms sold through the Army & Navy Co-Op in Britain are now with the Univ of Glasgow/Scotland.
The A/N Co-op used to assign and mark the firearms with a unique number in addition to the mfg ser#. That unique A/N # was what the Co-Op listed the guns by in their sales book(s).
Not all of the BSA and LSA commercial Lee rifles and carbines were sold through the Co-Op of course but a very large number of them were.
What the Glascow Univ archives will send you if they have record of your firearm is a copy of the ledger book page that your gun shows on.
Here's a link to the Univ webpage:
http://www.gla.ac.uk/media/media_67061_en.pdf
The Lee commercial (Lee Speed) were available with a long list of options. The bolt handle could be either the straight so called 'rifle' handle or the 'carbine' style with it's forward slanted handle.
5 or 10 shot magazine, Heavy or lighter SMLE weight bbl,,the latter after 1904. With or w/o top rib. All sorts of sight combinations, a tang safety (that works in reverse of what most would consider 'normal').
Several caliber options, the Metford cocking piece (no manual safety only a half cock on the striker) or the Enfield cocking piece with it's thumb/wing safety on the rear of the cocking piece.
You name it,,they'd make it for you.
Many are retailer marked with names like Rigby, Holland & Holland, and the other big names. But they are just that,,the retailers.
After 1907, BSA offered the Lee Sporting rifle with the SMLE charger bridge also. Using a MkIII action instead of the L/E or L/M, it will have a thumb charger slot in the left wall and no dust cover of course.
I have a 5shot Lee sporting that throws standard dia 303 sideways at 50yrds. It likes .313d bullets just fine.
Another Lee sporting I picked up that has been re-bored (I assume) to 35cal. I haven't done a chamber cast yet but I'm expecting a 35-303. Maybe I'll be surprised! For now it sports an SMLE Ishapore .410 bbl fits the stock inlet perfectly) and I use it occasionally for a few rounds of skeet. It'll feed a round from the mag so it's good for doubles!
I had another Lee/Speed,,a 10 shot that I sold some years back.Also a 303. Don't know why I sold it,,seemed like a good idea at the time. I think I bought my Martini Sprter (Watson Bros) in 303 w/a ribbed bbl to replace it. Still have that but haven't done much with it so I guess I'm about even.
Wyo,,very nice rifle,,is it set up for a 'scope? detachable mount bases on the left?