I think the magazine is not right for this rifle. Any of the Lee Speed rifles I've seen have all had the 5 round mag.
I have a carbine that is different from yours. The butt stock is as per milspec but the wood is incredible, lots of fiddleback etc. It once had a long range sight mounted on the wrist. I would love to find another. The bolt handle is flattened against the butt socket and it has an engraved metal action cover that is friction fitted to the bolt, like yours and is marked "Army Navy Society". The flattened knob on the bolt is marked with crossed flags.
The barrel has the metford style rifling and is a gain twist. The butt socket has a 1/8in wide engraving pattern on both edges and is marked "Lee Speed Patent, BSA Co. 1896". There is also a crown over the date. It also has the cut off.
I just had to take it out and shoot it. It shoots into about 4in at 100 consistantly.
It also likes heavy bullets at moderate velocities, such as 200 and 220 grain round nose. Lighter 150 grain bullets don't group well at all.
It kicks like a mule. Not at all fun to shoot with the heavy bullets.
Nice looking rifle by the way Gairlochian.