Just tried again with the machine at full working heat, cover off, steam boiler off, water alarm off, and the drip tray removed to get a good view of the overflow pipe and the components inside.
Before using it there were no leaks of any kind, no hissing or strange noises. I saw no leaks while pulling a shot although the entire water reservoir was still used to make one cup - all of the water discharged through the single overflow pipe. I collected the water in a tray underneath and it was cold. I don't know if this is relevant but water also came out of the steam wand at a reasonable pace despite being switched off. Whether this was just water in the pipes or indicative of the problem I can't say. There was too much water all over the place.
Whatever it is that failed, it took a few weeks. This has gone from wasting a little more water than it used to, to sometimes wasting a lot and sometimes none, to now not working at all.
From what you're saying it's more likely to be the pump, which means I guess it'll have to come out and be checked. Gulp....