Great summary, Petkow. I would just like to add a little more information about the O2 "Pay & Go" Tariffs and the "Pay & Go Bolt Ons".
Some of the o2 "Pay & GO" Tariffs include "unlimited" access to the "BT-Openzone" and "The Cloud" wifi networks. For example, check the "Simplicity Tariff" and "Text and Web for Blackberry" tariffs.
O2 - Pay & Go tariffs. Get 10% of top-ups back and surprises
Alternatively, a "Blackberry Bolt On" can add wifi access to some of the other o2 "Pay & Go" Tariffs for only 5 pounds!
O2 - Get a Pay & Go Bolt On for extra minutes, texts or internet
This is how to set up Wi-Fi on an O2 sim:
O2 | iPhone Wi-fi | How to set up Wi-fi on your phone