While I don't excuse this guy's behaviour, your reaction and posts seem to be overly dramatic, from what you've said I get that this isn't how you wanted to appear, but if this is representative of the way you communicate with him, it's probably not the best way to go about things.
He doesn't have to be listed at companies house, if he ceased trading as a limited company - and wasn't restricted in doing so - nothing to stop him being a sole trader as long as he drops the LTD status. As to selling cars, you could push the trading standards angle, but they are largely toothless in this scenario and have been cut to the bone in terms of staff in most areas.
When going to small claims court, the test is one of being reasonable. Is it reasonable to take a 7y/o car to a main franchise dealer for a generic fault that doesn't require OEM level diagnostics and pay £107+ cost of parts and any additional labour, relative to it's price/condition at the time of sale and when purchased from a sale trader operating off his drive? Probably not. This is likely basic work, your average high school kid with a multimeter would likely be able to diagnose - I replaced a door sensor earlier this year for £6.95 delivered.
At best you have the work done (you pay), you take him to small claims court (you pay), he refuses mediation and/or to settle so it goes to court (you pay more), you go to court (time off - claim for it, but again you 'pay' via lost holidays etc.), you win and obtain a CCJ, you then need enforcement (you pay) and if that's unsuccessful, you need to pay to escalate it (again, you pay). By now you'll have been dealing with this for months, likely invested days of your time in all of the above along with hundreds of pounds. If you think it's worth all of this over what is likely to be a simple/inexpensive repair, then have at it. Personally i'd send him a recorded delivery explain that you would prefer to resolve this without having to go to small claims court if it's a simple fix, but if he isn't able to arrange for someone to look at the car within 7 days, you'll arrange for an independent garage to get the work done and come after him for the money. He probably has a few hundred quid in this car, if it comes down to £60 for someone else to look at it and £15 in parts, then that's likely to be a lot easier to stomach for him than a few hundred at Kia (same brand who try and sell people £3xx of replacement keys when someone asks for a replacement shell for the fob).