One of my kids recently bought a SIM card from the airport machine for 5 or 10 quid. It was for Vodafone, and when he stopped in at a Vodafone store a few hours later to add some extra money on the account, the folks in the store told him that if he had gone there directly, they would have given him the SIM card for free.

So maybe if you don't need the capability immediately on arrival, you can save a bit of money by waiting until you get into London.