My opinion would be to get a degree.
As previous posters have mentioned, aviation does remain a very fickle industry. At the moment the airlines are recruiting from the schools to a high extent, however, there really can be no guarantee that this is going to continue. We could wake up tomorrow morning and find that another terrorist attack against aviation has occured or that the taxes on aviation have been raised significantly. There are many many reasons as to why the industry could collapse overnight.
I was once told, when considering what degree to study at University, that the most important choice is to choose a subject that appeals to you, and not one that you feel you have to do. The trouble with the pilot studies degree schemes is that the degree is strictly limiting - if you do the subject, you're almost narrowed down into what you can actually do with it.
Myself, I studied for a BA in History and Politics and really enjoyed my time at University as a result of studying a course that directly appealed to my interests. And as well as that, I now also have a back up position if the industry does cave in. One piece of advice that rings true though is that "all good pilots have a back up plan ready".
Just my thoughts on the subject,
Chris