Philpridd,
This is just my personal view, I can't speak on behalf of Adrian Flux (obviously there is no underwriter to clarify things at this time of day), but I personally don't see it being an issue if you were to start the insurance for the same day as the MOT and not before.
Firstly, driving without an MOT isn't actually an endorsable offence under section 47 of the RTA 1988. Meaning, you can't get any points, convictions or disqualifications, only a fine. Obviously, if you are on the way to a pre booked MOT, no fine can be given either. In its self, the fact that driving without an MOT isn't endorsable.
Secondly, under section 148 RTA 1988; an insurance company cannot invalidate a issued certificate to the point of making it a criminal offence, ie. driving a car that isn't insured to cover a third party risk, however, this does not prevent them from recovering costs from a third party payout via a civil law suit.
In short (and subject to my opinion), yes you can insure a car that isn't MOT'd, but you will only be receiving third party only cover until the MOT has been carried out regardless of the cover type you have paid for. Yet despite being covered, the insurance company are able to 'sue' you for the amount paid out were there to be an accident.
Has this helped at all?
Bed time for me,
Ed