Have you assigned the plate to a vehicle yet?
If so here's an extract from DVLA :-
Assigning a personalised number to a vehicle
You need to apply to DVLA to assign your personalised registration number to a vehicle. It can only be used on a vehicle that’s registered (or about to be registered), taxed and used in the UK.
How to assign your personalised number to a vehicle
Send your application to DVLA.
DVLA
Swansea
SA99 1DS
You need:
the V750 certificate of entitlement or V778 retention document signed by the person named at the top of the certificate
the registration certificate (V5C) or the new keeper supplement with a completed V62 ‘application for a vehicle registration certificate V5C’ form
an MOT test certificate for cars and motorcycles over 3 years old (1 year for heavy goods vehicles)
Pre-1960 vehicles need a valid MOT to assign a registration number.
You must complete a V62 form and return it to DVLA Swansea before applying if the new keeper supplement has been stamped by DVLA.
Conditions for assigning a personalised registration number
You can’t:
put a personalised registration number onto a vehicle displaying a ‘Q’ number plate
make the vehicle look newer than it actually is
Adding a nominee or taxing your vehicle when you assign the number
You can add a nominee when assigning the registration number by:
completing section 2 of the V750 or V778
enclosing the £25 nominee fee by cheque or postal order payable to DVLA (do not send cash)
You can tax the vehicle at the same time. You need:
a completed V10 application
a cheque (payable to DVLA, no cash accepted) for the correct vehicle tax
What happens next
Once DVLA gets your application they may need to inspect the vehicle - they’ll contact you if they need to.
DVLA should approve your application within 2 weeks and send you:
a letter showing the new registration number
a V948 authorisation letter that you’ll need to get your number plate made up
a replacement MOT test certificate for cars and motorcycles over 3 years old (1 year for heavy goods vehicles)
a new V5C registration certificate - this can take 4 to 6 weeks to arrive
Your application may take longer if DVLA needs to inspect your vehicle.
You need to tell your insurance company your new registration number.
When I bought mine many moons ago, we still had a local DVLA centre, and as the guys was doing the V5, MOT etc, I asked the same question.
I'm sure the answer was that once you have the new paperwork, you have a couple of weeks grace, to get the plates changed.
Good luck!