Your search will have been fruitless because there isn't any cable called "coex".
Virgin Media uses "coax" (short for coaxial) cable to bring TV and internet services into your home as far as the set top box for TV, or the superhub for internet.
If you want to connect devices to the superhub, in order for them to have internet access, you either use wireless (wifi) or ethernet cable, a common grade of which is Cat5.
BT does not use either coax or Cat5 cable to wire up your house. It uses bog-standard twisted pair cable that should not be used for hard-wiring your computers to the superhub or any other router.
If your fussy kids insist on a hard-wired connection to the router, then yes, you should have Cat5 (or ideally Cat5e for future-proofing) run round the house. To get it done most neatly you will need to have it terminated at face plates by the router and also in the rooms where your kids want to hide while they
download their HD pr0n play their games.