Gosh thank you, both of you!
This morning the flower was being held well clear of the water - to the extent that I was afraid of its being snapped off in the wind. I've never seen a hardy lily do that before but I suppose it is in very shallow water.
I've taken some more pictures to help (I hope) with identification, though I confess the first one is mostly because it's so pretty. It really is pure white, no suggestion of a blush of pink or cream.
The bud, now closed again, shows just how far out of the water it is now. It also shows that all the stems are pale yellowish green, and that at least the one to the flower is hairy. Filamentous algae have just invaded so it's hard to see how hairy stuff under the water is - everything looks hairy just now!
Then there's the underside of a mature leaf, which I'd call reddish light green or light terracotta. (Oh well all right: pink.
) And finally a shot of the whole plant(s) which might help with leaf shape.
Sorry - if I knew how to do clickable miniatures I'd have done those leading to bigger pix. And now I'm off to drool over, sorry study, all those wonderful pictures of waterlilies....