Well, I sent my application off for my new ADI Badge on 16 October 2010. It arrived this morning (28 October).
So in summary of the process, my CRB Check took 17 days and my actual licence renewal 12 days.
I must admit that I left it a bit late sending off my renewal, as I'd seen some information which said to send it in the month during which the current badge expires and to allow 3 weeks. Admittedly, other info said to send it 3-4 weeks before it expired. But all's well that ends well.
It's worth pointing out (as a reminder) that the letter which accompanied it said that the badge should be displayed at all times when giving paid instruction, not at all when another ADI or PDI is instructing, and should be displayed picture side facing inwards. It also suggests leaving it on display when the car is being used on test (I always leave mine in).
EDIT 30/12/2010: I've also put a bit about this process in the Useful Information section.