Agree with the above post.
Think about it; if BA only took pilots who came from an integrated school, don't you think the likes of Oxford and CTC would be making a MASSIVE noise about it in their marketing?!
"Go integrated or NEVER get into BA...fact!" (or something similar!)
They will only take low hours guys direct from an integrated school (specifically from Oxford/CTC/FTE via the Future Pilot Programme) but for direct entry all they care about is how you perform in the sim and at assessment, that is how they will judge you, not based on whic school you came from.