I note you said buying a ‘used’ vehicle, I went to do this many years ago so things may have changed but it wasn’t as worthwhile as I’d hoped.
For example a new £50k vehicle that’s VAT exempt costs you £41,667 so saving £8,333 (approx!)
A used vehicle that costs £50k you only get VAT relief on the dealers profit margin. So if the dealer paid £48k for the vehicle then he clears £2k, he then deducts reasonable expenses… rates, wages etc so he ends up with a profit of £1k that he has to pay VAT on, which is about £833 That is how much you’d save.
Now mines was over a decade ago and all those figures are just estimates to give an example so obviously speak to an expert but as far as I remember your wife could buy the car and be the owner while you’d be the registered keeper (like Motability & us) or she could immediately sell it to you? You can only get VAT relief once every 3 years to prevent the previous abuse & fraud that occurred.
Good luck 🤞