A340 rider,
I would think BA are not discriminating against you. I would say that the height issue will be to do with pedal reach on their aircraft. If with your shoes on you are over 5ft 2" then I would apply and bring it up in the interview (if you are lucky enough to get that far) BA may then make you do a functionality test on the aircraft that you are destined for (i.e can you deflect the rudder to full left then full right) If you are already eligible to apply to BA then this would suggest you already operate either the Airbus or the Boeing. So I wouldn't see your height as being a problem.
If I remember correctly the RAF had some weird arm reach test you had to whilst going through pilot selection. So even if you were the best pilot, if you're arms weren't long enough then you weren't taken on. It is all to do with the aircraft the RAF operate.
Good luck!
Right, now back to waiting patiently for DEP to open up!
Odd Socks