Apart from the usual FR24/ FlightAware suspects, for BA at LHR they have a fairly reliable (gates can change as Ops re-arrange) Wayfinder at:
https://wayfinding.maps.ba.com/departing
This both gives the best indication of the intended gate, and a step-by-step route to it.
The tunnel is a good alternative to the crowded transit - you can either walk it all or make use of the travelator