I'm pretty sure that's wrong, from
www.gov.uk/personalised-vehicle-registration-numbers/take-private-number-off
After you apply
Your original number plate will usually be reassigned to your vehicle automatically, if your application is successful. This will happen straight away.
You’ll be sent:
a new log book (V5C) showing the vehicle’s replacement registration number - it can take 4 to 6 weeks to arrive
your original MOT back (if you sent it to tax the vehicle)
a V778 retention document if the private number is in your name
If the private number is in someone else’s name, the V778 document will be sent to them.
Before you can drive your vehicle, you must:
put the original or new number plates on the vehicle before you drive it
tell your insurance company your new registration number
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Taking private reg off new
Taking private reg off new