Tax will be automatically renewed and the Direct Debit payments will continue to be taken providing an MOT is in place at the point of tax renewal. Payments will continue automatically until you tell DVLA to stop taking them or you cancel the Direct Debit with your bank. Valid insurance should also be in place for vehicles registered in Northern Ireland.
So a change as as far as I am aware to tax a vehicle it required a vlid MOT and insurance and certainly when I have renewed at a Post Office they have scrutinised the insurance certificate.
"Don't think of them as problems, think of them as opportunities."
"OK, I think I've hit an insurmountable opportunity!"