One of my former cow-orkers used to work for the debt-collection department at British Gas. I suspect you may well need a lot of luck.

That said, merely not swearing and making death threats will probably put you in the top 3% of callers by politeness, so they might be somewhat amenable. Here's hoping.

It's looking good at the moment; I phoned them after their specialist team didn't ring back, and although they aren't 100% on returning phone calls they apparently have come to the same conclusion as me about the origin of the bill oddity. So hopefully the hard part (convincing them I'm right and they're wrong) is past and it's now just a matter of them issuing a corrected bill and me paying it...

IIRC one friend of mine got so annoyed with them in the end that he went to their office and sat in it, refusing to leave until his problem was sorted out. I would have liked to have seen that.