Originally Posted by
WillTravel
From what I remember, it would be extremely difficult to walk through the tunnel that separates Heathrow from the rest of civilization.
I've been told it's theoretically possible but against the rules. If anyone sees you they have plenty of time to catch you while you're in the tunnel with nowhere to escape. When they got rid of pedestrian access to the north side of the airport they made bus rides free from the airport to its vicinity so that airport workers would still have a free way to get in.
If you absolutely want to walk out of the airport, it should be theoretically possible to take the free HEX to T4, follow the walkway to the Hilton, and walk out from there along the roads on the south side - but it would be a heck of a long walk and, other than the Hilton which is way above your price range, you won't be near anything useful. Or you might be able to take a car rental/remote parking shuttle to that lot and walk out from there on the north side. I don't consider either of these to be a practical option.