I haven't studied them in detail, but BAA's and Dixons Travel's return policies suggest that you have 60 days to return the item if it's in an unopened, re-sellable condition (unless faulty). Unfortunately since that's not the case, they probably won't issue you a refund.
The consumer contracts regulations would cover you for 14 days if you bought it online, by phone or by post but that's not applicable in this case.
The only slim chance you'd have of obtaining a refund is if you could argue that the headphones are not of satisfactory quality as described under the SOGA 1979. However, this comes down to a subjective judgement on whether the quality of the headphones is reasonable or not. If they had pairs you could test at the shop, Dixons could probably argue you knew what you were buying and therefore they are of reasonable quality.
You'd also have to go back to Heathrow as you'd have to take it up with Dixons Travel. Depending on where you live, it may be a waste of a little time or a lot of time.
All in all, your chances of a refund unless it's faulty (did you try these headphones before you bought them to know if your pair is defective?) are quite slim. It's a lesson learned, and next time, buy a pair before you fly
