Success. "Update Updater" pop-up gone.
If anyone has the same problem with pop-ups telling you to update the Updater and get blindman again, the answer is spelled out in another thread, and has worked for me with no more problems.
Reinstal (don't need to uninstal first, and no need to redownload the whole thing), but making sure to deselect the green tick on "Download updates immediately" part way through the instal wizard. It tells you you already have it installed with the green box ticked, but uncheck it anyway and it works.
I needed a friend to help find the instal icon before being able to do this, and I needed them to explain that reinstal doesn't mean redownloading the whole thing...
The problem seems to have been caused because I'm on dialup. Is there any way SPYBOT team can have a note to tell people to uncheck this box if on dialup to save future problems please?