private motorists always need insurance cover, minimum of Road Traffic Act (third party), where you are going and when makes no difference at all, you need insurance.

It is legal however to drive a viechle not displaying a current Veichle   
Excise Licence (tax disc) to and from a pre booked MOT test.

An idea might be to get the garage to send a mechanic to collect it, as he would have trade insurance that would cover them.

All licenced Mot Examiners need a valid driving licence for all veichles
they examin, in case their rolling road breaks down.