I don't know whether, as a BT Broadband user, I'll get free access to BT Sport, but I suspect not and would have to fork out for BT Vision. Oh well.
You do (as long as you're currently in a contract with BT[1]).
http://www.bt.com/sport/You can watch it online for free via their online player.
You can get it added to BT Vision if you have that (we don't).
If you've got Sky you can get it added to your Sky card for free. (We have a Sky box but use it as a Freesat box as we don't pay Sky anything month to month, and BT were still able to add it to our Sky card, you just need the viewing card number.)
1. Our contract had lapsed and we were on a rolling monthly doodah, so it was a good reason for me to sort it out. BT bill went down too as I chopped off the services we weren't actually using (some of the call packages, including International).