o2's offer of wifi is that of btopenzone and now its own so any usage at home on your wifi is ok.
O2 wifi is free to all and is rolling out to more places.
Does this mean I cannot access the wifi in my house (which I already pay for!)?
No, your home broadband wifi is free (bought and paid for as you said) and you can use it as much as you like.
To use O2 Wifi when away from home is free for everyone and you can register for that here:
I think d444nyc misread your question.