Ok working on the assumption the OP is using T5 I think the few manned staff travel desks have now moved to Zone E (centre of the rear wall of departures level, beyond the self service machines/commercial check in desks, midway between the entrances for North and South Security) they are labelled “ Flight Management” and possibly “Rebate Travel”...there is no longer a staff travel standby room.
Not sure about the exact deal with non BA staff but the very first option is usually to try checking in using the booking ref/PNR using one of the automated machines, if that doesn’t produce a seat and leaves the OP on standby then I’d suggest they should then head for one of the E zone desks...if in doubt there will probably be some lurking staff around who might be able to help out.