Not much! I think there is only one sponsorship scheme available at the moment, that is through CTC. I have an Aeronautical Engineering degree from Imperial College and I dont really think it ever helped me get into aviation. It is all down to other skills, mostly interpersonal ones that any potential employer is going to look for. However, the degree does look good on an application form and may help you get an interview, after that it is of less use.
Good luck.