I think 1 hr 15 is cutting it very fine, and its down to if your flight is on time and did another plane land just before you, adding to the immigration queue. Immigration will be the main issue, not customs.
DOnt forget that ona big plane like this, even if you land on time, its usually another 15 - 20 min by the time you hav taxied and got off the plane. That only gives you 50 min to make the next one.
If you do book it, my advice would be to book the BA flight because AA and BA havea corporate link so it might be smoother getting your bags switched through and you should be able to get your boarding cards for the BA flight, not sure if they will do that for BMI. As long as you buy a single ticket you should be OK to get your flight moved if you miss the earlier one, if you buy two tickets, they dont have any responsibility, so thats another key point, one ticket.
One other thing, you could check to see if there are better connection times via another airport. I wouldnt recommend Heathrow as you'll have to change terminals and immigration queues would be much worse, Gatwick there would be only a short terminal change, possibly you could check via Paris or Amsterdam as well?