A Martini action you mean?
No you wouldn't be able to use LR in it.
Chamber is quite a bit larger in diameter. Bore dimensions are a bit smaller than the usual for a 22WMR too, though the action would handle the pressure OK.
It'll make more of a mess than you need, if you really want to eat what you are shooting.
If it has a decent factory barrel in it, it'd be a shame to #### with it, really. The factory barrels were about as good a barrel as has ever been put on a target rifle. They were not supposed to leave the factory if they would not shoot less than an inch at 100 yards.
Buy a decent barrel and have it installed. It'll take a bit of fiddling with the extractor as well when it's chambered. Track down both a barrel and an extractor, and you could make it a convertible.
Or just buy a 22 Mag.
Sell the BSA as is, and you could buy quite a nice one with the proceeds, I think. If it's in decent shape, anyway.
Cheers
Trev