A re-bore to 1293, 1310 and 1330 is classed as a service repair and is not a modification. A bore to 1380 would need to be declared.
Remember, BMC used to do a 'Gold Seal' replacement engine which had been re-bored to the next size up and these came without the new capacity being declared anywhere. So the BMC Dealer would just fit one as a repair.
It's when you do work which is clearly obvious, like fitting twin SU's or a supercharger that there is an issue. It could be said that any BMC camshaft is a standard option as they could be supplied new and were homologated as standard.
With classic cars an owner doesn't necessarily know what he has. I sold an Innocenti which was at 1330 cc after it's re-bore, but the V5 says it's 1275 cc and it is not a requirement to change it after re-boring so long as the engine number stays the same.