No problems for me. Have you checked to see it is on 3G and not auto-connecting to BT openzone wifi networks? There are so many BT networks in central London that you are almost always in range of one, and the phone automatically connects.
For me, the problem with BT networks is that even after I enter my mobile number to register, the iPhone joins the network but there is no internet connectivity which means web pages start loading but never finish and you don't get any 'not connected to the internet' messages. I tried at length to get o2 to sort it out with no success so now I have given up and disabled them (connect to a BT network, go to settings > wifi, tap the blue arrow by BT openzone, tap disable auto-connect).
Since then my browsing when I'm at work has been both BT- and problem-free.