Good plan. However, as Whitenemesis already said, statutory rights are one thing, enforcing them is another. Have you checked out the vendor's reviews in every source you can find? Have you checked Companies House records to see how long the company has been in business, who the company officers are, and what their previous/other directorships are?
Worst possible case, you have it inspected, there's plenty that needs doing, more than you can afford or are prepared to spend on it, and the vendor refuses to help. Can you afford to take the car back, leave it on the forecourt and hand over the keys, and wait a couple of years for the case to be heard?
Best possible case, it's well-nigh perfect and you're a dog with two tails.
Most likely case, there are things that need doing, and the vendor isn't willing to help, so you pay for what's needed, keep the car, and either file a claim (and wait a couple of years) or not, depending on how much you've spent.
(I'm being realistic, not pessimistic; there are honest dealers, but in my experience most will do all they can to avoid spending or refunding anything once you've driven away.)
It's the Dirty Harry question; "Do ya feel lucky, punk? Well, do ya?"...