Hey,
You didn't mention what qualifications you have? Do you have AAT or similar? Sage/bookeeping skills?
I'm in a similar position to you at the moment. I wrote a thread about this in this section not so long back and posted Anon and I can tell you I totally empathise with you!! There are loads of other people in the same boat so don't feel like you're alone. (And that's me included) I've been claiming JSA for just under a year now and it's getting me very down aswell. Right now I'll settle for any job I can find- the only setback is, I can't seem to get myself a job.
I don't know what your furthest qualification is but it might be worth studying for a bit longer and doing a part time course like Creepy suggested. I'm also applying for admin/accounts jobs like yourself and I also decided that I didn't want to go to Uni despite the tons of flak I got from my parents.
I enrolled at a college in September this year. I'm studying AAT part time/ two evenings a week. It will take me 3 years before I'm a qualified accounting technician but it's well worth it. AAT is widely recognised (by almost all Accounts firms in the UK). It may be that the qualifications you currently have aren't good enough on paper. A-levels alone don't seem to get people that far these days.
With regards to AAT. I can study this course part time at my own pace and still have loads of freetime. By June next year ( after final exam results) I should be able to get a job in this field. If not, most definitely when I have passed AAT III which will take a further year.
I'm experiencing great difficulty finding a suitable accounts job but that's understandable as I haven't got any experience let alone any accounts qualifications as yet. It's also been very hard to gain voluntary experience but again that's not too surprising.
I have many family members and friends who don't have a degree but went by this route and are in very good jobs.
Whatever you decide, goodluck.