The system is still "fuzzy" in the case of cars which are in theory eligible for MOT Exemption, but not yet Tax Exempt (Historic Class). Consider the case of the mulberry car. It was built in Feb '79 according to the chassis number, and first registered in April '79. It is therefore over 40, but not eligible for tax exemption till April 2020.
Now in May this year, due to the fact that it was suffering from a running problem, it was SORNed and the MOT had expired. In May the running problem was apparently resolved, so I wanted to take it off SORN so I could take it for a test run or two. (I still planned to take it for a voluntary MOT once I knew it was ok). So I went online, and the system refused to allow me to tax it, without a valid MOT.
I contacted DVLA and they said that as the "build date" on the V5 is simply shown as "1979" then they wouldn't consider it MOT exempt until 31st December 2019 (notwithstanding the fact that it had been registered in April '79!). They offered to change the "build date" on the V5 to the exact build date, as long as I could tell them the build date to an accuracy of the day.
At this point I gave up, drove it to the MOT station SORNed and MOT less, then re-taxed it online as soon as it passed the MOT.
So the problem is now resolved (though anyone else in the same position could have the same problem), and next year it won't be a problem as the car will be Historic Class, so the system should work correctly. But it does mean I didn't in fact get "MOT Exemption" from my car's 40th birthday.
The lunatics do seem to have taken over the asylum......