As I understand it you are referring to two separate conditions, zero cost taxation and MOT exemption:
For the purpose of taxing the vehicle you do not need to make the declaration of exemption from MOT, ie 'no substantial change', (V112), if you have an MOT performed, (tax is still £0).
The vast majority of vehicles manufactured over 40 years ago are automatically exempt vehicle taxation fees, although you still need tax the vehicle at £0.
If you choose to declare the vehicle exempt from MOT you need to convince yourself, (and the local force should they pull you over), that the vehicle has not been substantially modified. (You make this declaration, it will be up to you to substantiate it).
Of course the perceived level of modification can also have a great bearing on your insurance company's opinion should you make a claim.
All of the information is available on the gov.uk website and as your position regarding the level of modification could be questioned I'd suggest you became familiar with the facts in readiness