That 3 pc 'limit' is little more than a "covering their backs" type clause in case they catch you trying to run loads of machines off a single connection (like in a block of flats).
ntl don't have the resources (or ability) to know or care if a normal domestic user happens to have 5 pc's connected in their home instead of three.
Most routers have 4 or less Lan ports - so to connect more machines than this you need to expand one of the ports out into a switch [like the one you have ordered].