Free MOT retest if garage is fully booked?

If my car fails the MOT, I take it away, repair it, then take it back for a retest, I understand they have to reduce the cost to a half price "partial retest" (and I've known some garages do it free). But what if when I phone for the retest, they are fully booked long enough for the 2 week period to expire? Sorry, this is for the UK, I didn't realise this was an international forum.