Sorry to hear about your bad experience, and I quite understand your emotional reaction and sympathise with it. However, as others have said, emotion is likely to harm rather than help your chances of getting your money back.
As you have said that the money is not really what bothers you, I don't think going after these guys punitively will make you feel better. Instead, it will most likely take up a good deal of your time and energy, and keep this nasty experience in the forefront of your mind for weeks or months to come.
Even second-hand car dealers are not necessarily totally evil, and quite possibly this was a simple mistake or oversight. I would approach it from this point of view and send them a polite letter stating the facts, including supporting evidence, and suggesting a reasonable amount of compensation. This may do some good.
Unfortunately, it may also have no effect at all, and the dealers may simply say that the car was fine when it left them, or that brakes are not covered by their warranty. Mentions of lawyers and Trading Standards may leave them quite unmoved. I imagine second-hand car dealers hear that kind of thing fairly often. They know you don't really have the money, time, and effort required to bring them to court, and that even if you did, your chances of a good result are slim.
I suggest the best thing for your happiness and peace of mind is to take it no further, but chalk this one up to experience. Second-hand cars are a proverbial minefield. I don't exactly start from the assumption that the dealer is trying to rip me off, but I assume that any part I can't see or check personally is kaputt, and factor this into the price.
As C.S. Lewis wrote, "Experience is a brutal teacher, but you learn. My God, do you learn."
