Charger cable warranty?

I got my iPhone 5s about 7 months ago from EE on a contract, I have 2 iPhone 5+ lightening cables and both have began bunching at the top and one has become defective by only charging when its in a certain side. I have warranty on my iPhone 5s so does that mean I can take the cables to the apple store and get them replaced? The previous cable is from my previous iPhone 5 that has no warranty.

Also I have read that if I do take it to store (if it is still possible) I'd need my iPhone's receipt? I don't actually have a receipt I only have my first bill which is in my mothers name. Does this mean I'd have to get my mother to come with me?

Here is an example of what I mean by both of my cables bunching:

https://9to5mac.files.wordpress.com/2014/08/screen-shot-2014-08-22-at-10-47-48-a m.png

The cable that has stopped working also has black bits like this over the connectors:

http://forums.macrumors.com/attachments/img_0807-jpg.468548/

I am certain that both the cables are genuine apple cables as I got them with my phones.

I would appreciate any help anyone can give! As a student I don't have the money to pull out for a new cable!