I studied art as a mature student at Central Saint Martins. I did a part-time degree and was also working the rest of the week. Before that I did a BTEC in graphic/web design and 3 D animation.
I now work part-time using my graphic/web design skills in a marketing role and run my art practice the rest of the week.
There is no doubt that if you want to be an artist you are almost certainly going to have to complement your work by doing something else.
I don't regret it at all though as I know I would have thrived in a job that does not have a creative aspect.
The type of careers that would be open to an art graduate (although you might need to complement with an MA in a more specialise discipline):
working in museums/gallery/auction houses; working for the Art Council; fashion buyer/designer; art teacher; art therapy; interior design; jobs in fashion/television; graphic design and illustration; working for community projects running art activities; animation (if you have computer/technical skills); curators...
There is no doubt though that these are competitive jobs and that opportunities and salaries are limited.
I think people choose art if they are really passionate about the subject and have the type of personality that can cope with the ups and downs of having a creative career.
I would make a really bad accountant, doctor or banker as I know I would not sustain this type of work...so these careers were never suitable for me anyway.