Thanks all. There are possibly a few things here that are assumed, but I don't in fact know.
In particular, FifeingEejit's "...it's still press-fit..." suggests that I could actually put the same cranks back into a BB from a different standard, provided that it fits the shell of course. I come from a world where a different BB type means new cranks. I'd just taken that for granted.
Given that, we don't necessarily need a new crankset. I'd agree, though, with citoyen's assessment that the left crank is probably for the scrap heap. We could keep the right and change BBs, it seems, although I hadn't realised that - but FifeingEejit's comments imply that another brand of crank might be more reliable. Nonetheless, the core issue is a crank that comes off, and I'd simply associated that, perhaps wrongly, with BB problems. Certainly, the first time, half the BB came out as well - but that could have been effect and not cause. And there's the creaking, but some articles suggest that all press-fit types can do that.
Giropaul asks a sensible question about budget, the answer being that this is a decent bike but over five years old, so we're up for a new crankset and BB (if needed) as normal maintenance/wear and tear, but not to getting into territory where a new bike would be more sensible. You'd hope that £100 would cover it (with Dad providing free labour, obviously).
So, in summary, I think we need a new left crank at minimum. I share with at least one of you doubts about whether it's a good idea just to replace that, and thus stick to a weird system. So that's a new crankset (I'll hope to swap the rings, if I can get something of the correct BCD). But, if we're doing that, and there are doubts about the BB30 system, do we go the whole hog with some kind of adaptor and a different system?
I did look through one or two guides before posting. I'll read the Bikeradar one again. I realise from those that not all BB standards take the same axle size/length, but none of them said explicitly that you can swap standards for the same crankset, even sometimes.