Neil Drapkin
I have a sharon fruit (fuyu persimmon) plant grown from seed
about 5 ft tall, several years old. It has suddenly become infested with white woolly blobs a few mm long on underside of leaves and on the woody parts. So far there is no sign of damage, and I can't see an of these things on adjacent plants. Any ideas what they might be, and how to get rid of them?

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That looks like an infestation of scale insects.
Information and advice here
https://www.rhs.org.uk/advice/profile?pid=557
Hope that helps 😊