I've been allowed in the JFK CCR even though flights hadn't posted but JFK and the angels there are different than LHR.
no harm in asking at the CCR reception provided you'd be happy with a 'no'. I am not sure "BA" can easily put you on a "list". Apparently there is one in case someone doesnt have their CCR card on them but I would imagine that explaining your situation to the angel (possibly with your TP balance on your phone) is as likely to yield entry as calling BAEC and asking them to send a message to the CCR.
as said, best to accept / prepare for being told 'no' until all TPs post.