Transfer plates via dealer

[dmacw]

Hi,

I bought a second hand car from a dealer down south. It was a bit of an impulse, so hadn't sorted out retention of my private plate in advance, prior to trade in (it was on a real old banger). My private plate is more sentimental and doesn't have a huge value.

Anyway that was 3 weeks ago. He was due to post up the new tax disc (he has paid, I've checked) and new plates ready for the transfer, but that seems to be "missing in the post" for 2 and a half weeks. He tells me he has checked the tracking number, but never seems to have it to hand. Twice in the last week he has said he'd call me back but hasn't. I've called the DVLA and they have received nothing. Seemingly that has gone missing too.

I did do an HPI check prior to purchase and it was clear.

So, frustrated tonight, I've called the DVLA to request a new V5c for my old car (which the dealer has), and have filled in a V62 to request a V5c for my new car (the dealer wasn't the previous registered keeper, I saw that before purchase).
My plan was to then do the transfer myself and then forward to paperwork back down to the dealer as we had originally planned.

However I've now spotted a problem - how can I transfer the plate without the MOT for the old car?

Any advice?

Cheers