Firstly, why should BA restart their sponsorship scheme when there are thousands of wannabes (far more than the industry needs) prepared to pay the whole deal, including type rating, themselves? Their accountants wouldn't be too impressed if the company proposed paying for something they don't need to!
Secondly, BA is recruiting only a tiny number of ab-initio pilots at the moment, and is doing it through direct contact with the three integrated schools (OAT, Cabair and FTE). The vast majority of their recruiting is for people with type ratings and a minimum of 400 hours on type.
If BA ever do reintroduce a pilot training scheme, it is very unlikely to be a sponsorship. It is far more likely to be on the CTC model, where you pay for your own training through a huge loan which is repaid from salary - assumimg you pass and are subsequently employed. If you fail, the loan would still have to be repaid...
Scroggs