If i already have a wifi connection, do I still have to pay to use Xbox Live?

I'm not very good with gaming consoles and internet and stuff like that but I have an Xbox and want to use xbox live. I read somewhere that you have to pay something like �45 a year to have a connection or something like that. Do you still have to pay that yearly fee if you already have a wifi router like BT Homehub? IM SO CONFUSED!!! :S