I'm a developer and have been professionally for 12 years, and I've been hiring and recruiting developers for the past 8. I think you first need to define what sort of role you'd like to end up in. If you want to work for a large company (a Google or a Microsoft) then a degree is definitely necessary. If you want to work for a small company then not so much. Assuming you don't mind too much where you work (at first, at least) then I'd say it's far more important to be able to demonstrate your abilities. A degree is good, but I've met plenty of developers with a degree who couldn't code, and several without degrees who are experts. If you can demonstrate your abilities through real world examples then people will generally take notice. For example, you could write some apps and release them to the stores, or contribute to some open source projects.
I
Ian Newson
@Ian Newson