I want to move my router. Does anyone know if BT can supply a longer cable to connect router to box?
BT won't supply one but you can buy one from Ebay or Amazon.
It is just a standard Cat5E Ethernet cable. The colour is entirely irrelevant.
It was just to make things simple for folks, older hubs had a red WAN port. No idea why they still send red cables, probably because they have a large stock of them.
There is absolutely no significance to the colour of the cable.
Would it matter if I use a Cat 6 cable?
Loads on eBay
Cat6 will be fine