So the scores on the doors look like this:

BA435 arrived about 40 minutes late at 1552, leaving a 48 minute connection for the 1640.

BA1352 then left 26 minutes late at 1706, arriving at 1810

BA1349 is due to leave at 2010, so no misconnect.

I'm going to guess that the OP made the connection, but would have been slightly squeaky bum depending on the amount of time needed to open the doors and sprint to the BP scanner.