Apparently Sony are running an exchange program for faulty PSP and PS3s. Even if it's out of warranty [Edit: May not work if they ask and you remember buying it more than a year ago....], as long as the warranty sticker is intact (you haven't opened the case to fiddle with the insides) and you've got the battery and charger then they'll send out a refurbished one via parcelforce and pick up your dud one to take back. This is all free of charge (less the phone call). It's said this even covers broken screens.
I noticed this while surfing eBay and noticed lots of people selling this info for anywhere between a couple of quid and twenty. After digging around a bit I found this handy info from a concerned eBay member..... http://reviews.ebay.co.uk/PSP-AND-PS3-REPAIR-SCAM-RIP-OFF_W0QQugidZ10000000004878687
Sony's number for this is 08705 998877, or try the cheaper geographic number 01923 653598.