In your position I’d mentally prepare myself to just get a hire car for a bit to cover work, etc, as a Plan B. It’ll cost a few quid but a lot less than £10k.
I also agree with the people that have said the dealer won’t be MOTing it until a sale is agreed.
The charitable explanation here is that there’s no incentive to do so on the dealer side, just to have the sale fall through for some other reason.
The less charitable explanation is that he’s trying to do you over for a few quid given you’ve said you want to drive it away on the day.
FWIW, I literally just bought a 10kish Ford and it was very much the same sort of thing. They did a bunch of work between my putting a deposit on the car and actually buying it a few weeks later.
So I wouldn’t automatically assume the dealer was trying to pull a fast one, but caveat emptor as always with used cars.