We have Sky for TV, but just use BT for broadband and haven't had any trouble. We brought our US Vonage adaptor with us, and use it heavily, and I have a slingbox at my dad's that I connect to, and for the most part, speed has not been an issue.
Every once in a while there will be a slowdown, but only enough to bog down the slingbox a bit, not the vonage or regular internet.