Unlike in the US, terminal transfers at LHR, other than for Flight Connections, are pretty well impossible. Therefore, for BA which operates out of two terminals, the departure terminal is set many months beforehand and passengers must check in and go through security at the correct terminal - they will be refused elsewhere.

If - and this happens very rarely - the plane to be used is parked at a different terminal, the passengers will be bussed from the gate, rather than told to go to a different terminal.

As to the gate information and ontime information, that is a different matter. The gate information will be accurate, when it is posted (which is usually not long before you need to get to the gate). But whether the flight is on time is about as accurate as anywhere else....