Sorry, Lizzie. I didn't notice your previous posting. I'm fine and I hope you are, too.

Regarding 3 I have had excellent coverage during my last stay in central London three years ago. What UKSteve intends to say is that 3 actually run only a 3G network based on UMTS2100. In contrast all the other British carriers also still have their old 2G networks (using GSM900 and GSM1800) onto which your phone will register once the 3G signal gets too weak. These old GSM networks, of course, provide very limited data speeds as the fastest data mode for GSM networks, called EDGE, delivers just 236 KBit/s.
But I don't expect that the lacking fallback to a 2G network should be an issue as 3's coverage in London is perfect.

Thanks for the clarification. Between my Note and my old iPhone 3GS, I'm sure something will work.