I would say it's impossible to predict with any degree of certainty. My wife/kids are US citizens, and we recently came through LGW and it took quite a while since the kids can't use e-gates. If you can use e-gates, it should be pretty quick.

The biggest unknown may be delays to arrival. The other thing I would say is that priority luggage rarely works on BA: if you check a bag, it may out by the time you clear immigration, or you may have a 10-15 minute wait.

tb