Admittedly this is somewhat out of date but I remember when I was passing through Oxford (about 3 or 4 years ago now!), BA turned up for a presentation and were asked about sponsorship schemes.
They said it was highly unlikely it would ever be brought back as it wasn't about getting "the best of the crop" but more about delivering a steady supply of low hours people.
With all the integrated schools full to bursting (one of our cabin crew said he wants to go to one of them but both the courses and even selection is booked out for months to come) it seems unlikely that the needs that drove sponsorship still exist.
The chap who did the BA presentation (who is still in charge of recruitment) described sponsorship as an outdated legacy of the days when BA was state run.
Still, anything is possible.