Transferring a Private Plate

[Aysedasi]

Hopefully someone in the know can answer this for me....

My wife has a private plate on her car. We are in the process of buying her a new (used) car. We've done the research, have test driven the model she likes and have put down a deposit on a car at a dealer some miles away. Although she hasn't seen it, it's been 'vetted' thoroughly by my son who is in the trade and lives close by the dealer. But as I'm off to Le Mans shortly, we won't be going up to hopefully finalise the purchase and part-exchange until 20th June, but I need to think about taking the plate off of her car ready to be transferred to the new one when we get the V5C for that.

Should I do this now? Bearing in mind that I no longer have the original plates (they disappeared in our house move a couple of years ago) we would have to continue to drive it on the private plate. Or should I wait until we get to the dealer, finalise the deal and then make the online application to retain the plate?