Needless to say, I'm now (finally) running 10.1.1.
After such an exercise in frustration, they should invent a frustration category for the next Olympics. I'd surely be a winner.
Thanks to either a dodgy ISP or dodgy 'phone infrastrructure, I finally managed to use Software Update to redownload 10.1.1.
And that's all I needed to do. I did move the existing bits of 10.1.1 package from the /library/receipts directory first.
Anyway, it's hip, it's happening, it's groovy, and stuff.
So now I get to look forward to 30-odd MB of 10.1.2 in a few days. Hmm. Think I'll go visit a friend who has broadband :)
Thanks again for your assistance Mr Sinclair!