If it's faulty within the first 6 months, then it is considered to be faulty at delivery, (you don't have to prove it). Under the Sale of Goods Act you are entitled to a repair or replacement, at no cost, (even for returning the device), or inconvenience to yourself. This contract is with the retailer, and is separate to the warranty.
Many retailers seem not to know or choose to ignore this act, but they are all bound by it as it is law, no matter what they put in their own terms and conditions. If their T&Cs contradict the Sale of Goods Act they are illegal in themselves.
I have been down this road and did eventually get somewhere, but it can involve some time and effort, depending on the retailer, and how much they value their reputation.
If you don;t get anywhere and you're desparate, consumer advice and trading standards can also help and advise.