I took them back to sports direct tonight and they said that they cannot exchange them without the receipt, box or a copy of a card statement (she paid cash).
She insists that this is wrong.
Unfortunately, it's your wife who's in the wrong. Sports Direct are under no obligation to give a refund, especially after six weeks.
You aren't legally required to produce a receipt to get a refund, but neither is the trader obliged to offer a refund, replacement or credit note AT THIS STAGE. Had it happened after a couple of days, then fair enough, but in this case it seems like it's tough titty. They would have a fairly good argument that the goods were of merchantable quality and fit for purpose at point of sale and for a reasonable period afterwards, but six weeks? I doubt it...
The only thing that you could do is raise it with Adidas UK, but I suspect that you may have no luck there either - I suspect that they may not be genuine UK spec goods. I once bought a pair of what appeared to be Nikes from Sports Direct and while they have lasted there is absolutely no way they're the genuine article.
Lots of good advice HERE