You have full rights over the product, an exchange is accepted without a valid proof of purchase, although the tags weather attached or detatched would be an advantage, the Sales Of Goods Act states that you have 7 days to return faulty goods. Before a purchase can be made by a sales assistant the product must be:
...Of a satisfactory quality
... very very similar or as described
... Fit for purpose
If a retailer suggests you can't return faulty goods they are committing a criminal offence.
Hope this helps!