It's no big deal going through the tunnels on a bike; there are rubber speed bumps every 30 ft or so, with a wide slot right in the middle for your two wheels to pass through `unbumped'. Mind you, if you get a head start and are mid tunnel before the traffic lights release the traffic behind you, it can be tad disconcerting to hear the bump-bumps steadilly getting closer to your back wheel! But the tunnel is simply not wide enough for a car to pass a bike so inevitably, when you pop out the other end, you are leading a convoy.
It has to be said that while around T4 & T5 there are good cycle paths that is not the case for most of the airport. On the Northside the T5 paths just fizzle out and you are left mixing it with everyone else, with the added hazard of a tired road surface with many cracks and holes. Aside from a pamphlet showing the routes, Heathrow actually does little for the cyclist - probably because they can't find a way to make money out of us.