Got my new iPhone yesterday. Took it out last night and was surprised I didn't have permanent internet connection - I had to keep connecting to the pub wifi. Thought the whole point of the thing is that it had internet connectivity! Or am I wrong? The only time it works properly is at home with my home wifi - but that seems to defeat the point. Am with O2.
When you are outside you have a permanent internet connection over the O2 mobile network (3G and Edge). Otherwise you can use wifi from the Cloud & BT Openzone or anyone else that might provide free wifi.
This page explains it: http://shop.o2.co.uk/update/wifi.html
The G3 network is not that Universal in the UK, but the Edge network is. You should always have internet access as long as you can get a signal. As stated, if you are in a building with thick walls or other geographical obstructions.