Approved Used cars normally come with a year's warranty. the law is on your side for the first 3 months after purchase if no warranty is supplied - the trader is required to prove that the fault was not there at the time of purchase, or fix the car FOC. the following 3 months you have to prove that the fault was there at the time of purchase, and if so then they trader has to repair FOC.
3rd party warranties are relatively inexpensive, and on something like a BMW will pay for themselves after one or two faults (at £100/hr you can spend £1000/day just on fault finding if something goes wrong). however, there are a few things they won't cover (electrical gremlins for example).
i used to have a 2005/54 A3 that i owned from new (was a factory order) and within 6 months of the warranty running out my climate control compressor went. Extended Audi Warranty = £500 at the time. Compressor repair = £600. I'd already lost out.
i wouldn't even think about a car without a warranty personally, especially German machines. one fault and you'll wish you had the warranty.
