Hi! Sorry if I've started a dispute. I certainly diidn't mean to!
I don't want to get rid of the flies - I like the idea of everything being part of a big food chain. They're just your basic houseflies, as far as I know. If the birds etc want to eat them, that's fine too (the flies may feel differently about that!).
Anyway, I've had a root around on the internet and it seems the Japanese rear flies specifically to pollinate sunflowers, so it seems the answer to my question is "Yes".
Well, I hope everyone has a great Bank Holiday weekend, with lots of sun for getting out in the garden.
All the best, Will.