My understanding is that there is no pedestrian access via the Tunnel Road from Bath Road to the central terminal area... That said, I've read in the past that the "side" tunnels (not the centre ones) do have a pedestrian pavement and it is physically possible to walk through them... that said, Heathrow's website is clear that cycling through the tunnel is not permitted, it's completely silent on the question of pedestrian access, and there are at least some anecdotal reports online that people have been turned away trying to walk the tunnel. ETA: Looks like others have confirmed it–perhaps best not to try this at the moment!

I think the safe bet would be to walk from Hatton Cross to Heathrow Terminal 4, which is definitely doable, and then to complete the walk by heading around to Terminal 5. Alternatively, you could walk up the Bath Road to the point closest to the tunnel and catch a local bus (free) to get the rest of the way to the central terminal area.