I've had my car a year and one week today, as it was a unintended purchase I hadn't taken my plate off my car so arranged it all via the dealer. Picked the car up on the Saturday, all paperwork sent on the Monday and by he Friday the plate had been removed from my car and by the following Wednesday my plate was transferred to my new car.
When they closed the local offices it caused major headaches but it's been swift since the backlog was cleared. Can't comment on how long it will take come March and September when the new registrations are released but I've not heard of any issues recently apart from PVRs fiasco.
Just a pain the it can't be done same day anymore, it's a right faff especially when your insurance charge admin for changing the plate.