If Heathrow Airport are keen on anything, it's getting passengers to use the shops. While they restrict passengers to their ticketed terminal, there are certainly reports of being able to visit a different terminal to make a largeish purchase. It won't hurt to ask. [edit] Ah, I see Gagravarr has given more detailed information!

You do have to go through security when you enter a terminal. The only exception is when you are connecting from a domestic flight. Whether it is the same security check as for originating passengers depends on the terminal - IIRC T3 and T1 use dedicated transfer security points.

It's been a while since I've done a connection at LHR, but it always used to be pretty easy to hop on to whatever bus you wanted. The difficulty is in getting back out of the departures area of the wrong terminal, as departures and arrivals are now segregated at T3.