The presence of a catalytic converter is not specifically checked at MOT, you just have to pass the emissions test.
For a petrol engine this includes CO, Hydrocarbons and lambda, measured by probes stuck in the tailpipe. I think it would be pretty difficult for an engine designed with a cat to meet emission standards with it removed.
For diesels, the only emission tested at MOT is particulates (smoke). It looks like you could de-cat a diesel, with a remap to take account of the reduced back pressure, and still pass MOT.