Not all dealers are a nightmare, my plate was switched from my old car to my new one and the original on my old car reinstated, all sorted out by the dealer with no fuss or drama.
How long did it take though?
My family all have 'private regs' and when they have changed cars they've been quoted 14 days for changing plates hence delaying the car! I normally do it for them at the DVLA office and it takes 10 mins although sometimes it can be 7 days but at least you can have your new car!
Took my docs in a week before, all ready on 1st Sep pick up, all cool. Did it through the Glasgow office of the DVLA when I originally got the plate and yes it took 10/15 mins, but I'm lucky that I have one of their offices relatively close, some don't. Dealer was hassle free, some aren't.
It's good to get it done in a week! Obviously an organised dealership!