My 17yo daughter applied for a provisional licence on the 4th May. She's still waiting.
She had a seizure 3 years ago and so after 12 weeks they sent her a medical form to complete. In late October, another letter arrived saying she needed to arrange a medical with the doctor. She's hoping to get the licence before she retires.
My son (no medical conditions) applied for his provisional and got told to send a paper form/picture in. Waited 3 months. Got his cheque back with no explanation as to why the application failed.
Applied again, second time it linked straight to passport photo, only had to provide a signature and he got license within 2 weeks!
As normy says - Seems they've sorted their shit for standard applications, but anything over and above its taking ages and you can't speak to anyone.