Finally got around to booking my NCT. Seems like I had the whole of next week to choose from so it seems like there's no delay at all at all.
Seem funny that we still have to phone in to get a booking. Didn't get asked for my super secret CCSN or anything. It can't be a database thing because afterwards, NCT sent me a payment link via email and once I went to payment page, I just entered my car reg and it knew who I was and just asked for the money.