I use a different approach, which does not rely upon dealerships and I find to be extremely easy. Basically, I follow these steps; 1) I take delivery of the car with the normal dealer assigned plates. 2) After a period of time (usually when the date prefix is no longer the ‘current’ new reg 😂) I do the online application to assign the private plate (no cost as the plate is on retention – see step 4). 3) I drive to Halfords and when parked in their car park I unscrew the plates and hand them to the technician, so that when they make up the new private plates they can drill the holes in the same positions. I screw the new plates on the car and drive home, storing the original plates in my garage. 4) Just before the car is due to go back, I do the online retention (£85 cost) and the registration number that the car had when I took delivery is always reassigned. As I already have those plates with the correct pre-drilled holes, I just swap them with the private plates at home. Takes 5 minutes. Total cost of the above is the £85 retention and the cost of the plates, and each process can be done simply at a time to suit me.
This is definitely the best way to do it, just need someone able to swap the physical number plates around