You must go straight to the MOT station by a reasonable route, no detour to a petrol station unless it's on route.
But there's no actual limit on distance as has been previously said.
So if there's no petrol station en route to the MOT station and I'm about to run out, I have to park up, take out my jerry can and get walking?

But then I'd not be driving it to an MOT station, I'd be driving it to a random street somewhere, so I'd still lose.