Was on the verge of emailing and saying I would pay what they said I owed, but emailed the accountant back and forwards (it took an hour), and it actually turns out that they owe me!!
I was the epitome of politeness and gratefulness towards the accountant who took time to explain what invoices had been paid and when. I completely ignored her trying to pass the buck onto me for the way it's all unfolded (much in the same way that he tries to pass the buck when he makes a mess) and just concentrated on the facts.
And it paid off!!
It's going to make a big difference, along with my holiday pay from my other job, to what's coming in at the moment!!