Englishal
You are right that loads of common spamcans will get to FL120, though it might take a while
Even so, the number of real IFR tourers in the UK is way way more than a "handful". There must be hundreds if not more of SE planes that can get to FL180. Any IFR tourer with an IO-540 in the front can get to FL200 or so. Oxygen is an issue but a portable Aerox kit is a few hundred quid, imported from the USA.
The stuff about a CofA is, IIRC, that any plane
capable of being on a CofA is not allowed to be on a Permit. This is a plain blunt revenue stream maintenance measure by the CAA.