I too had only been self-employed when I started as a signaller, and if I gave my honest opinion on how NR HR dealt with the situation I would probably be self-employed again PDQ!
Anyway, enough doom and gloom. Are you still in touch with your last place of education? You could try there I suppose, or if someone gave you a few days piece work, or even the Job Centre maybe. Just keep waggling pieces of paper in front of HR until they bite. It worked for me!
Above all don't lose heart, you'll find someone to give you a reference sooner or later
