See Donald Starchan has a good overview. The short answer is
First is that you can get a sim at the airport or via any cellphone store in town. The main issue is what plan to get. You have to go through all the carriers and here was the data as of last summer which I updated looking at the sites
O2. O2?s best prepay plan for visitors is called Pay & Go Go Go. The prepaid bundles depends on how much you top up for 4G pay & go go. Add £15 credit for 75 UK talk minutes (to UK cellphones and fixed lines), 500 texts, and 1GB of data, valid for a month.
They also have an international add on so u can call back to the US cheaply at 2 pence/min and 10p/text although with this much data using skype probably makes as much sense for calls and use google voice for free texting. You need to sign up for a free international plan by calling 2202 for free or text LINK to 21300 to switch to International Sim.
Tmobiles has to be the easiest I've seen to provision. Just text them. The 25 pounder is kind of a no brainer.
T-Mobile’s prepaid data add-ons are known as Smart Packs. These are prepaid usage bundles that come in three grades—choose the one you think most likely corresponds to your usage. The cheapest costs £10, is valid for 30 days and includes 1 GB of data, 100 minutes of domestic calls, and 400 domestic texts. For £15, the inclusive bundle offers 2 GB, 200 minutes and 600 texts. At £25, it’s 3 GB, 500 minutes and unlimited texts. To activate a Smart Pack from a T-Mobile SIM simply text SMART10, SMART15 or SMART25 to 441. To call back to States, add the free International Pass to any other pay as you go plan, text INT to 441. You now get 5p/min voice and. 18p for text. So O2 is way cheaper overseas and about the same for uk costs. But it is convenient.