They won't nick you in that time, and if they do just state the circumstances and you should be OK!
(ie the gestapo at the post office wouldn't let you tax it cause of the MOT!)
If your MOT is booked you can drive a non taxed vehicle to the test station (err directly!

) without tax, as you need the MOT for tax purposes in accordance with the SORN/road fund rules.
As I'm away a lot of the time I see this come up again and again, and in my opinion if you have a history of paying, intent to pay, on your way to the MOT etc, then you have no worries!
Hope this is a bit helpful!
(BTW I guy i know once rode a Ducati with no tax or MOT from Northants to Devon perfectly legally because it was booked in for an MOT in Devon-yes it was me!!!

)
So long as you are not breaking the law intentionally you have no worries IMO!