We were there last July and found O2 to be the best company for a short term plan. We didn't require a lot of minutes but wanted something to be able to make some calls and texts and have data on the iPad. I think we spent about 20 pounds or so. It wasn't a lot over 4 years ago
Try contacting your provider to set up the SIM card, or you can just get a very cheap pay as you go phone once there for like 15-20$ That's what I did-b/c when I asked about the SIM card they said it would just cost more anyways...Hope this helps! I know a lot about London, England as well as I used to live there, so if you have anything else to ask, don't hesitate.
Cheers! over 4 years ago