If they took your name and addy there should be no problemo. I have gone back to Currys with an item after eleven months and they found my purchase on their computer.
Legally you do not have to produce a receipt, even if you are given one and there are huge signs up in the shop saying it is required. A judge ruled that they do not legally have to give you one so why should you produce it? Only makes it easier to keep tabs on stuff.
You dont have to provide a receipt if you arent fussed on what you get back in return for your product.
For exchanges without receipts it is down to the shop if they wish to honour such things with a "replace like for like" or gift vouchers, or store credit.
They do not have to give cash.
Warranty repairs... no idea, but exchanges and refunds, yes... you dont need one, but dont expect cash in return.