I'm not sure, But I suspect consumer rights shit (probably sales of goods act) means you should be able to request a replacement or refund, as the computer you have isn't fit for the purpose sold, and they've not repaired it in a timely manner.
I think it depends on the age. I doubt you'll get a refund but I guess if you shout at them, or get a general consumer watchdog/magazine/pc gamer to shout at them for you, because bad publicity is good for things happening. you don't ask you don't get.
If another engineer turned up and bolloxed it up I'd be knocking him upside the head with the entire pc, but that's not likely to get you anything except arrested.
Hopefully it won't break again anytime soon. I tried to get a new PC out of them but they were really insistant on trying to repair it... at least its fixed.