Anything you purchase from a trader has to be 'of satisfactory quality'. European regulations state that electrical goods need to remain fully functional for at least 2 years to meet this standard. So, there is no doubt that you can insist on 'having things put right'.
Your right to a replacement item, however, (rather than a repair) only extends to the point at which you are legally deemed to have 'accepted' the goods. If the item hadn't worked as soon as you'd got it home then you could have demanded a replacement. Equally, because you don't normally use all of the functions on a new device straight away, the 'pre-acceptance' period probably goes on for several days (or even weeks) after you've made the purchase. This is why Comet allow a fairly generous period of 28 days during which they will, without question, work on the assumption that you've never formally 'accepted' the goods. After this period they are fully within their rights to operate a 'repair only' policy. Sorry!
Chris