Not quite true, there is no case law on this, but H O guidance indicates FAC required for rifled tubes for shooting use in RIFLES, thus if you have an early .303" Lee Enfield with (eg) a .22 sleeve, or a 7.92 Mauser ditto, or a sporting rifle that you use and for which you have a sleeve so that you can practise on a 25 metre range or similar, then the adaptor is held on ticket because it is held for shooting. Presumably if you had a 2 pr or a 6 pr that you wanted to shoot you would need to put the sub-cal on ticket to allow you to do so.
This is essentially the same as putting an antique on ticket for use, even if only for blanks. Adaptors for shotguns, eg .410/12 bore etc are not required to be held on certificate at all.
This is because adaptors are not firearms, ie lethal barrelled weapons, nor are they components, because the firearm functions perfectly well without them. The only lethality about a 2 pr sub-cal would be if it were used as a club to hit someone over the head, and in such a case it would be rather less handy than any other item of wood and steel, eg a carpenter's claw hammer.
Alan1.