I have cable broadband - so I was able to ditch my BT line.
VoIP phones have an IP address - but this can be a private IP address behind a firewall. What this means in practice is you can "log-on" to your VoIP account from anywhere in the world (just like Hotmail) and make and receive calls via your account. So for instance I willl shortly have a 020 7 London number linked to my VoIP account. That means if I was in an office in New York, and I was logged into my account on a VoIP phone, then if you called me on my London number it would ring in New York. And the caller would just be paying a local call as if I was in London.
0870 numbers are free with VoIP; but soon you can pay a fee and have geographical numbers. Plus your supplier will take a small cut of your outgoing call charge. But some big players are coming into the market and they are sinking millions in. But as more and more folks have a VoIP number - then there is less money to be made as VoIP to VoIP is free. In the end phone calls will be just like email - FREE - apart from your connection to the web.
You do NOT need a router for a VoIP phone - you can plug it directly into your cable/ADSL modem. Plus many VoIP phones have a 2nd ethernet socket for you to then plug your computer in. VoIP phones can be "hardphones" (sit on you desk) or "softphone" (software on your computer).
It's actually quite easy. Try:
www.xten.com - VoIP softphone FREE
www.gossiptel.com - VoIP supplier