While the BA Cadet Pilot scheme is still referred to on their website, it does not currently exist and it seems unlikely that it will ever resume in the format it took before 9/11. There is no news to suggest that any BA Cadet scheme is likely in the near future.
Check the Archive thread on Wannabes - Professional Pilot Training for lots of information about the types of courses and their costs, the timescales involved, and the experiences of those who have gone through them. Expect to pay somewhere between £45,000 and £100,000 depending on which route you take, and how long you take to do it. An ATPL can be achieved whille in full-time employment if your employer is flexible. In fact, on that note - I've a feeling that you can do much of the course at the BA Flying Club at Booker, near High Wycombe, at a BA-subsidised cost. Check your internal staff information for more details.
Scroggs