At this point, it will probably be easiest to wait until you’re in London and then go to a Vodafone or EE store there to buy a prepaid sim.

You usually get the best deal and plan options that way versus buying at the airport or trying to buy one online.

Going to a store there is usually a relatively painless process because prepaid plans are much more common there than in the US. The people at the store will usually set it up for you and they know all the tricks to make sure your phone gets registered correctly because they do this stuff all the time.