I assume that you mean "Cable" broadband, because NTL provide both Cable and ADSL (via the phone line) services. The distinction is very important because it dictates the type of router that you would use.
Essentially, to share the broadband connection you do need a router. It is possible to connect the two PCs directly and use Windows' built-in Internet Connection Sharing, but this is not ideal - the connections can be unreliable and the "Host" PC which connects directly with the modem must be running for the "Client" PC to have internet access. A router is definitely the preferred option.
With a router, both computers connect directly to it and get their internet access over the LAN from the router. With a "wireless" router, the connections can be by ethernet cable or wireless or a mixture of both. Often one PC is located close enough to the router to use a cable connection. With a laptop, a "wireless" connection gives it portability and, with a PC that is too far from the router for cabling to be practical, it can also benefit from a "wireless" connection.