An MOT and roadworthyness are two different things. Once an MOT certificate is issued it's valid until it's expiry date but as you say all a valid MOT really means is that the car met the standards required at the time of issue. If you test a car with a vaild ticket and it fails, technically it still has a valid* MOT cert but roadworthyness would depend on the reason for failure, for example not meeting emissions specs isn't going to make it dangerous to drive but something brake related on the other hand...
I've had a couple of vehicle retification notices in my youth for various things, you have to then go to an mot station who will check the fault and verify the vehicle has been fixed then to the cop shop with a bit of paper to prove it.....