Q: My Apple TV 3rd gen won't restore in iTunes. I have been through the process multiple times and purchased new leads ensuring they are data leads compatible with this device. The white light is flashing quickly. No Apple Store locally so £59 down the drain

Has it been restored or is the issue that it is not appearing  in iTunes?

If it's appearing and going through the restore then theres nothing wrong with the cable, that indicates a hardware issue.  You would need to take it to Apple at that point.

AppleTv has a standard 12 month warranty - do you remember when you bought it and possibly if it was with a credit card?  If you know the card Argos might be able to track the transaction and issue a duplicate receipt - if it's less than 12 months old Argos should replace/repair it.

Good luck with it.

Also if you run into issues have a look at the links here and contact Apple:

https://www.apple.com/uk/support/appletv/contact/

Here's the warranty info:

https://www.apple.com/legal/warranty/products/accessory-warranty-english.html

I tried 4 Micro USB cables before I found one that wasn't just a charging cable.  It took < 10 minutes once I had the correct cable...Thanks.