This 'entity' appear to take seven times as long as necessary to do anything.
Considering pilots pay for the licence, pay for medicals and pay to see their consultants one wonders how this is permitted?
The loss to the industry of otherwise fit pilots must run into £millions every year.
Once they have exceeded what you consider is a reasonable response time I would suggest a letter the the Chief Executive. At least then the letter would come down from him into the Medical Department.
The more letters he gets, the more annoyed with this entity he will surely become.