As I left KX, after my third trip on the tube, I checked the card and it
said I'd been charged for 3 lots of £1.70 (itself a bit of a shock - my
mental image is still around the £1.20 level). But that's £5.10
altogether. Shouldn't it have been capped at £4.70 [my first trip
started at 11.30am], or does it only get recalculated overnight?

It should be capped as you go along provided you always touch out properly.
I take it you are 100% sure that it didn't actually cap you? I've never
been capped so don't have experience of how the machines display your
journey history when you have been, but they aren't a model of clarity even
for uncapped journeys. I can well imagine it listing three £1.70 journeys
but actually showing that only £1.30 was debited for the last one.