Graham, think yourself lucky, mate. I had problems with the Moving House and the Billing teams, ending up with them continuing in charging me for services at my previous and my new addresses concurrently ...despite their engineers visiting to reconnect us at the new address. My problems lasted about 9 months in total.
As you say, it's annoying that one team seems to know nothing about the other, and is unable to intervene when necessary to fix customers' issues. It felt at times that one team would be blaming the other, and then washing their hands of the issue. I tried saying that I didn't care how they sorted it, as long as they did sort it. My problem, as far as I was concerned, was with NTL, not with a particular department nor team within the company.
Anyway, glad it's sorted for you now. Keep an eye open for any gremlins after you've actually moved