Your treating physician needs to supply the AME with a report, answering all the items on the CAA template for this, that needs to go via your AME to the CAA.
They will then invite you to come and see their psychiatrist.
If they are of the opinion that you are fit to return to flying they will report that to the AME and they can sort out your flight status.
Commonest issue is that that report to the CAA does not address all items and you then end up in a bit of a loop until that is sorted, and there can be a bit of a wait for seeing the CAA psychiatrist.
So how long will it take is difficult to answer.