Since suitable power leads were already in use when I felt the need to mess about with the Raspberry Pi, I plugged-in a phone back-up battery. And, strangely, the Pi worked fine. It ran for the hour I was using it, with no signs of running out of power, so this may have been a useful discovery for future use.
Or, perhaps not, since the battery wouldn’t power a screen. Well, not a reasonable sized one. Further experimentation may be necessary.