>My BT broadband package came with a router, as most/all of them do. Is this different from the type that you describe?

At the very least, to be able to use broadband you must have a modem. The modem lets you attach to your provider's network, but it does not provide a hardware firewall, or allow you to use more than 1 computer with the connection.

I believe that some "integrated" devices are starting to appear, that is they are a modem and router combined into a single box. AFAIK these are still uncommon in North America - I don't know if things are different over on your side of the pond. Over here you typically get just the modem with the service - either they provide it as part of your monthly fee, or you buy your modem and get a slightly reduced monthly fee. If you want a hardware router you have to buy it and install it yourself, although this is very easy.

Probably the simplest way to be sure would be to Google the make/model of the device you're using to see if it's just a modem, or if it integrates a router as well.