but at 550m ATC protects to CAT III, so ATC in the UK assume you're doing a CAT III at that RVR.
Not necessarily so, as you stated there are few airports which have CATIII capability, mostly have only CATI, sometimes an intermediate CATII.
But the minima is based on
any aircraft being capable of making an approach without the use of augmented automatics being available such as required for an autoland to be carried out.
Thus these RVR minima are based on arbitrary trigonometry so if our wonderful CATIIIB aircraft has for instance an engine failure or hydraulic system failure rendering it incapable of its CATIIIB capability, at least we can determine if we can make an approach using the published minima for RVR using a CATI approach, like any other (non-)commercial plane could do if unable to fly better then CATI, and have a chance of seeing some approach lights to determine the possibility of identifying the correct runway to land on.