Road Vehicles (Construction and Use) Regulations 1986 ... Regulation 26 - if you can find a copy of it.....
Some info:
ETyresMichelinAll the research I've done in the past on this subject, has only found info about tyre construction and usage.
I can't find anything about wheel types.
The fact that tyres must be the same size and construction (cross ply vs radial etc...) on the same axle automatically means that the diameter must be the same, and the wheel width, must be, by default, more or less the same (for the tyre to fit the wheel properly).
Regulation 24 covers space savers, but that's a whole different tin of worms ....
Spares are not covered by the MOT - even if you have one.
This is on the theory, that as soon as you use it, Regulation 26 applies.
All the MOTer can do is advise you verbally, if it's illegal - i.e. worn, bulging, different size, etc... assuming he even looks at it.
MOT - scroll almost to the bottom.
Car Owners Guide.