Did mine last month. They couldn't read the attachments on my mail - some IT screw-up - so even though I had a case number they just ignored it.
I phoned after 10 working days, and the customer care team were great in rectifying - they had it turned around and ready by the following day. Wrote to the head of licensing and also very on the ball and receptive to feedback.
This was for the first issue of a card-type license, for my PPL. No skills test etc. needed.