Now, this would depend on where you live (although you used a £ symbol so I can guess now actually...anyway). In America, apparently it is very important to get a degree for the airlines to even consider you, but in the UK, a degree isnt essential. I dont think a computing degree would be particularly helpful for a pilot (that said, I'm doing computing A level, you could help me out haha) but it may get the airlines to look at your CV. Then the question is, do you want to work that hard for a degree, and get in that much debt, just so some guy looks at your CV for a bit longer? Well, it may mean the difference between getting a job or not, but, it may not.
£21,000 may mean the difference between being able to afford the training and not being able to. Personally, I'm still debating on whether to go to Uni, or to spend the £20,000 or whatever on training fees...become a CFI, get different flying jobs, then eventually apply at an airline.
Anyway, back to your question. The problem with going to an aviation school is that you have nothing to fall back on if you cant make it as a pilot, for whatever reason. At least, with your degree, you could
become a programmer.
If you want to fly for a living, have you thought about jobs outside of the airlines? Getting a job with the airlines would be difficult, but how about an instructor? Flying 'flying doctors' around (I have a friend, here in the UK like me, whos mum works in a flying medical plane, thing). I dont think the requirements for these jobs are as high, and I dont think they require an ATPL, please correct me if I am wrong (which, I accept, I probably am). That way, you can build hours, and then maybe pay for an ATPL, and get an airline job, should you want it. It all depends what you want to end up doing, and how you want to get there.
I hope that helped, and I hope I wasnt coming across cynical or anything.