OP he

Thanks for all the *very* useful responses so far. (Notable that
nobody has recommended a "treatment" (i.e. from a bottle)!)

I think one of my main problems has been that there has been far too
much crud in the bottom of the pond for years, which may have provided a
nutrient factory.

We had fish for a while, but I gave them away when I realised they were
eating all the tadpoles and also all our snails. *However* I couldn't
catch one of the fish, and it stayed there for the last two years: I do
believe that that has had an adverse effect on the pond (which is quite
small - only about 3m by 1.5m by up-to-.75m deep). Unfortunately (for
it), the recent hard winter killed it, so that problem has gone away.

I've cleaned the pond, and I'm now filling it with water from the rain
butts. This new start, plus the advice received here, may help us
achieve a much better balance. I need a few more plants too, possibly:
the pond is in full sun.

Thanks a lot folks!

John