Having done new entrant recruitment at BA I can tell you that as long as you have a work permit in your passport and can prove that it is renewable then you shouldn't have many problems.
I took on a couple of people who didn't have EU passports.
At the end of the day what's gonna happen if you apply and they don't like your passport? You won't get the job! They won't amputate and limbs or imprison you...
Give it a go!