UA and AA flights use T3. Assuming the BA flight is from the U.S., it'll most likely arrive at T4 which is a runway across from T1,2&3.
Easiest place for the 2 arriving on UA and AA to meet is the seating area immediately right as they leave the customs hall and meld into the waiting throngs. The pax arriving on BA should make him/her way to T3 by taking the Heathrow Express (every 15 mins) to T1, 2 & 3 and wait, look for them in this area.
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