My understanding is that the min conneciton time for LHR is 90 minutes. We connected T4 - T3 and it was not too bad. We would have been ok with 65 minutes -- this was also an arrival on 1/1 when there was less traffic.

If you are booked in premium class on AA (business or first) and your BA flight is in the same record locator, AA may meet you at your BA flight and transport you to T3 flight connections.

--Jim