They will fail only if there is some visible defect such as a major crack, piece missing, or the wear is so extreme that on ventilated disks the ventilation holes are showing through. That won't happen until the total wear is 6mm or more. Checking the disk thickness is not part of the MOT. Shortly after buying it with 33k miles on the clock I skimmed the disks on my Focus on my lathe when I fitted new pads. They were worn by 2mm which is actually the recommended wear limit but after skimming they look brand new as far as any MOT tester is concerned (including the one who tested it sometime later) and will continue to give perfectly good service for another
30k miles. Hopefully more in fact given how light I tend to be on brakes. Maybe the previous owner was hard on them to wear the pads and disks that fast.The recommended wear limit is more about selling you another set of disks than any actual performance measure of the disks themselves. There is a huge safety margin built in before any degradation of braking performance takes place.
-- Dave Baker