A few of the plants in my conservatory have masses of cotton wool-like growths under the leaves and on the leaf axils, what is this and what is the cure?

The growth is a means of protection produced by mealy bugs, which often repel insecticide sprays.

Forcibly spray with a fatty acid based insecticide.

If this does not work, you will have to resort to biological control, namely, the mealy bug predator cryptolaemus, this will eat both the adult and larva.