That would be an urban myth.
BA could not offer cadetships "on the quiet". There are many many good reasons why they could not do this. Not least being:
a) There is no budget for it in their accounts,
b) It would break the law regarding advertising and selecting people for jobs,
The fact they were doing it would leak in about 5 seconds in the world of flying training providers - and it hasn't.
Urban myth.
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