Hi Sam,
Well done on getting to this stage - how far along in the application process are you?
First of all, have you checked that you’re entering your details correctly? If so, from my own experiences, your license should appear on the DVLA system for you to view at some point after your medical. I remember checking a day or so after I did my medical and every day subsequently and my details appeared roughly 2 weeks afterwards.
It is simply a case of someone in the DVLA obtaining your successful medical results, putting 2 and 2 together and updating your records on their system.
MM