Thanks. Although there was a heart-stopping moment after I'd put the battery in when nothing happened (is there a capacitor which needs charging, perhaps?), it sprung back to life, and it was eager to get out & working.
I took a leisurely walk to work this morning, meandering through the back streets of Bermondsey, and getting some great shots. Such fun.
Meanwhile, I can tell you that the problem with your Minox was not the battery. The aperture ring should move freely (and prehaps it's sometimes too freely) at all times. Not doing is a sign of something wrong, and I have to say my understanding is that the Minox 35s are not very repairable. Not that I've ever needed to find that out, though I did strip down the one which was smashed on the street (remember those wrist straps, folks!) out of curiosity.
Hope you're able to find one that works soon.