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Oliveover - you're still well within warranty. The Sale of Goods act protects you against what is obviously an inherently faulty laptop. You need to contact HP, who must deal with it. After 1 year it's the shop's responsibility. HP should also reimburse you for any postage costs as it is their fault for basically selling you a piece of... 
... self-combusting technology. While you're there, mention any other faults the laptop has had. It might have been a dud one from the start in more than one area.
Khvegas, I don't know if you're still within the cushy warranty period of 1 year. After that, things get sticky, but you're still protected by the Sale of Goods Act for up to 6 years with your seller, with diminishing returns on what money you can get back. Whatever you do, DO NOT settle for vouchers, or for paying £229.00 to get it fixed as PC World thinks is appropriate to charge for laptop repairs on faulty laptops they sell (ka-ching!). You are covered by the Sale of Goods act which means they have to repair or replace with no cost to yourself. You might have to fight it, but don't delay and don't give up hope. Consumers need to stand up against companies peddling expensive, easily-breaking things or it will never get better.
The company may refuse to repair it as it's too expensive for them to justify doing. That's fine. Again, they cannot offer you vouchers or substantially less than what you originally paid for it (unless you've had 5 years slave labour out of it). Look on the Which? website for details of draught letters. I popped in "faulty goods" into the search-box and got to the draught letters very easily. If all else fails, you can Rescind the Contract and they must pay you the money out in cash. Remember, you're protected for 6 years.
In all of this, I am assuming your harddrive is still ok. Rather than risk getting a completely blank computer back, please keep reading! It's still accesible, and easy to get the information off of. If you have a friend with a spare Sata harddrive connection (I'm guesing it's Sata, you can tell that when you've got it out) on his/her computer, a screwdriver, and a big external harddrive to save things onto, you can take out the harddrive from your laptop and get the information off of it. If you don't feel comfortable doing this, I am sure a little local computer shop can easily do this, but you're going to need somewhere to store the information.
Good luck!! I know exactly how frustrating this is as it's happened to me. I'm back to using an old, reliable laptop without sparkly graphics but one that hasn't failed me for 8 years. They don't make them like they used to!!!
