What chance do I have?

For a bit of background, I did not really know about PE / the finance route when I was 18 and I went to a non-target school and did a law degree (which I enjoyed to be fair). Since starting working after, I have settled in restructuring / distressed advisory and I really like the PE side of it, often dealing with PE boutiques who buy companies in financial distress etc etc.

The problem is that obviously now I want to get into PE, I did not go to a target university, I did not do a finance degree (although I am working towards my accountancy exams at the moment). 

What would you suggest I do to get into the PE business - even boutique firms? Do you think I would have a chance? I'm not too fussed about going to the big firms as I have basically written them off as options already due to the previously mentioned problems.