Although the crazing appears to be on the inner surface, I’ve seen it suggested it’s actually within the polycarbonate material rather than on either the inner or outer surface of the lens. If this is the case, then IMHO cleaning or polishing would be unlikely to remove it.
it might be worth doing an internet search on ‘polycarbonate headlamp lens crazing’ or a similar search. Some of the search results will hopefully cover the effectiveness (or otherwise) of cleaning and polishing. If you do attempt polishing out the crazing, then ensure you apply a protective UV coating as a final stage (can be bought as an aerosol spray).
Sorry, i don’t know whether crazed headlamp lenses would result in an MOT fail; if the headlamp(s) light output and beam pattern isn’t affected then I don’t see that it should, although that’s just my view. It might be worth asking at a local garage that carries out MOT testing for their opinion. My last two car’s headlamps had very minor crazing and they both passed years 3 and 4 MOT’s without issue, but the crazing was very minor.