After getting an Arts based degree you can move on to other courses. There are lots of courses out there an it is about finding the career pathway that is right for you. You may not know which way you want to go yet !
The Royal Academy offers a 2 year fully funded course but this in highly competitive with 15 places a year. The Drawing schools offers a year funded drawing course.
Sotheby's offers courses in Business, logistic and arts management.
The Courtauld Institute of Art has wall and easel painting restoration courses which have a scientific approach to art.