There is almost no shopping available landside at LHR, so unless you're connecting at LHR, you won't have access to the shops. (There are a few dining options and usually a WH Smith or Boots or something landside on arrivals, of course.) I know T4 has a SIM vending machine (and would guess most of the other terminals do as well), but I would guess that those won't be very data friendly for you. I think you might be best served by figuring out if Carphone Warehouse or some other major shop near where your staying carries a SIM that will work for you and bring directions to help yourself get there from LHR.