The answer squarely depends on the time of day.

It is perfectly doable via the FCC when there is only a 5 minute security queue. However early morning and late afternoon the queues will be much longer than 5 minutes and I don't think you will be eligible for Fast Track (AA elites aren't, can't remember if BA elites are or not?).

As MajorVoid rightly says you can be off your RJ flight and in the T1D Terraces in 10 minutes if you run.

You don't strike me as the running type however Smirnoff...