Congratulations Ds3
I found the skills test a huge ordeal too, and it took a few weeks to recover from it!
I took my paperwork to Gatwick in person the day after my skills test (be there well before 0830 though as the slots get taken up very quickly) and handed over my documentation and fee. Two weeks to the day, I received a phone call to say it was ready for collection. I don't think there is any way of making it any quicker than this.
I understand that whilst waiting for a licence to be issued, you can still fly under your instructor's licence privileges.