The Brits liked to mark their bore sizes by the smaller bore diameter. The US convention was to mark them by the diameter at the grooves.
Their designation for the .22LR was .220 Long rifle. Take a .220 bore, drag a rifling cutter through it for .0015 to .002 per side, and you are at .223", or .224".
Still not a bad idea to slug it, though. Best to know what size it actually is, as it'll help when it comes time to look at reamers.
Pilots on the 22 centerfire reamers are listed at .219, more or less (by tenths of a thou).
A CF barrel, these days is .224, mainly. CZ is still making Hornets on .223 barrels, if James Calhoons website is to be beleived, and there have been lots of CF wildcats made on Rimfire barrels. Downside of a rimfire barrel is the twist rate is typically 16" (20" for .22 Short) and will not stabilize heavier bullet well. Rimfire barrels are typically made of somewhat softer steel, as well.
Light bullets and light loads, though, and rimfire barrels have held up pretty well in practice.
A BSA rimfire barrel is worth enough to be not worth considering as a prospect for a rechamber anyway, though. Barrel blanks are cheap enough. If it's already butchered <shrug> owners choice!
Cheers
Trev