An AME (aviation medical examiner) can revoke your medical at any time, and they will know who you doctor is as part of your regular medical, and they will confer. However, other than the annual class I medical by an AME, the onus is often on the individual to make the decision whether or not to disclose interim health issues to their AME. As part of pilot training, it is made clear that any change in your health that may affect your flying must be referred to your AME.
The problem is that for many pilots, particularly in the low cost carrier segment, if you have no medical, you have little or no income so there is a financial penalty to disclosing any medical issues. In addition, the amount of debt a pilot can incur as part of their training is enormous, and can make the average student loan look like a drop in the ocean.
I did find it interesting that the P2 had only 630 hours despite being with the carrier for two years, there were questions to be answered there, and it seems he had been on extended medical leave if the reports are to be believed. i would nt say a pilot with 630 hours is particularly well experienced, as initial reports stated. We should be very wary of any reports other than the BEA's own. The BEA have a mandate to provide a factual report free from subjectiveness and assumption, and that should be the primary, if not the only guide as to what happened.
(Completely coincidentally my own AME was on the BBC News just now as part of a report.)