I passed my skills test and sent off my licence application and it took 3.5 weeks to come back.
I have continued to fly while waiting for my licence, but yes I am still technically a "student" as I don't have the piece of paper to prove otherwise so I have to pay an instructor £40 an hour to "supervise" me when I disappear xc and cannot carry passengers... I'm sure I don't remember it being this way when I got my driving licence but it was so long ago that I can't remember.