To fail an MOT the brake pads need to have less than 1.5mm of brake pad material left. To make that easier to understand, 1.5mm equates to the thickness of a 5pence coin.
Brake discs are a grey area when it comes to MOT standards. When I sat my MOT tester course, I was told unless the discs are seriously weakened (I.E. you can see the vents (For vented discs); there are cracks in the disc face; or the discs are wafer thin (For solid discs)) as long as they pass the brake imbalance tests and do not grab or bind then they are a pass & advise.
However, you MUST understand that the standards for the MOT test is very low and just because they pass the MOT, it doesn't necessarily mean they are in good condition meet service standards.