I've had the same thing with short MOT when getting tax. Been refused and argued to no avail. I said I had it booked in for an MOT, but needed tax before then as it bridged the end of the month but they dug their heels in.
As for whether you need MOT for getting tax, it's not related exactly but it does give the authorities a way of checking that vehicles do have a valid MOT. That's my understanding anyway. Same with Insurance.
It'll all be academic if they bring in numberplate "spy chips"! Oooops, sorry, that was in MCN so it's probably b*****ks
