Whats the procedure for buying a 2nd hand car?

You'll want to see the MOT and V5 (new form is called the V5C, IIRC), and if they're in order, hand over the cash. The V5 should list the person you're buying the car off as the registered keeper. You'll need to fill out various bits on the V5, and take a slip from it with you, along with the MOT.

And a receipt, and I know you just forgot. :-) Mike.

Not forgetting insurance if it's a drive away.....

To be honest (And with all respect) if you're that naive about car buying, either have an extremely knowledgeable friend present or an AA / RAC type bod to see if the car is sound

So the dealer or the private seller would give me the V5 and it is up to me to fill it in and send it off? Or do I have to do it and hand it to them before I get the car? So if you buy a car from Daves Dodgy Banger Car Company, it should say so on the V5?

Again with the insurance, nobody is going to check it are they? Up to me to get it.

If it's a dealer, they don't need to put their name on the V5 - it'll be the name and address of the person who owned the car before the trader bought it. The V5 is filled in, you get a little slip from it to keep until the seller posts the original back to swansea and they send you a new one. I'm not 100% if the seller has to fill anything out on the V5, but there are instructions printed on the back of the form. I also imagine there's plenty of info on the DVLA website.

Nobody's going to check, unless you drive past a police car or an ANPR van, but if you get quotes before you go to collect the car, it's just a matter of ringing the insurance co on your mobile and telling them you want the cover to start immediately.