1: 'The same fault keeps occurring and the garage is unable to fix it'
Write to the car maker asking for technical help. If this fails, ask the dealer to buy back the car for the retail price, or to swap it for one of similar age, mileage and specification.
2: 'My car isn't as described'
If the car has been misrepresented, you are entitled to get your money back or, if you are otherwise happy with it, you could negotiate a partial refund.
3: 'My insurance company won't pay up'
Write to the boss of the company, outlining why you think your claim should be paid. If this doesn't work, take your case to the Financial Ombudsman.
4: 'My warranty claim has been refused - they say it's wear and tear'
Make sure the offending part hasn't been thrown away. Then arrange an independent inspection by an automotive engineer for a second opinion.