I cannot give out 'legal advice' if you know what I mean however if I were personally in this position I would do the following.
Write a letter outlining the series of events, dont be emotional just factual - times, dates, payments etc and send it recorded delivery (keep an audit of everything from now on so recorded delivery backs this up in court). Importantly, provide the timescale for resolution - 10 working days from receipt is reasonable in court and your required resolution (be sure what you want, you cannot change your mind later!)
Whilst you are waiting for trader to reply - send a letter of complaint to Trading Standards (the local TS covering the area of the trader). Contain a copy of your complaint letter as sent to the trader (this will be handy in court, they like TS to be involved). Also ask TS if there have been any reports of the trader forwarded to the OFT - Office of Fair trading - keep a copy of this for court.
Await the reply (or no reply).
Once the timescale you provided is up, forward another recorded letter to the trader. This time inform him that you have received no reply (alter to suit), that you have reported the case to their local TS and that as a good will gesture, you are giving them an additional 5 working days to resolve amicably. Also include the fact that you know your rights under the Sales of Goods Act and are willing to rigorously defend said rights. Make sure you send this letter to Trading Standards so they can keep their file up to date, also call them to inform them of your next move.
It may now be worth getting the car independently inspected, get the report and forward to the trader and TS. Win in court and you will get all your costs plus some.
Response - yes/no?
Dependant on the if the trader has resolved. Draft a 'letter before action', provide an additional 14 days for the trader to resolve, at this point, you must make it clear that will will seek full refund for the vehicle, plus expenses and costs via the court unless an arrangement can be made - templates readily available. Send a copy of this to the TS and call them to inform them.
Review your docs and ensure a full audit trail. Ensure everything that you incur as an expense or loss is detailed. Take a walk to your local court and talk to them, review the fasttrack process online then follow the guidance. Tell TS that you are taking them to court
Sit back, wait and let the games begin. For many traders, it suddenly becomes real when they receive court papers
Good luck, keep cool, dont let emotion cloud your judgement and importantly - stick with the facts and only the facts...