I'm not at all sure that the debt only arises when it's billed - it would be worth taking legal advice on that point, perhaps initially from Citizens Advice, but they may not get involved if it's a business matter. It might be worth posting this point in the legal section of this site.
The key thing is not to acknowledge the debt in writing - that will extend any statutory limitation period.
Ask for a copy of the letter of engagement that you should have been given at the start. The accountant cannot impose any terms that have not been notified to you before the contract was entered into. I'm guessing that he didn't send you any terms and conditions - efficiency doesn't seem to be a strong point - so that will get you off the hook as far as that rate of interest is concerned.
It will be interesting to see your answers to Jaydees questions.
For the accountants on here, I've come across this before. I was approached by a local trader a few years back who was concerned about the self assessment deadline, some three weeks later. It turned out that the accountant (Chartered) had only done one set of accounts, and that was nine years before, and he hadn't sent ANY bills apart from a small one for the VAT registration. When we got the tax returns from the Revenue we found that he'd put round numbers in, based on the VAT records that the client had maintained. It wasn't far out, but I was amazed that the revenue had accepted this for so long.
He never did send a bill,and we turned round two years accounts in three weeks! Not bad in January, bearing in mind we had to work out the opening balance sheet from scratch.

The client had pretty good records, fortunately!