There appears to be a grey mould forming on the surface of our house plant compost.

Is this likely to damage the plants?

The greyness is unlikely be harmful to your house plants.

It may be due to the peat content of the compost oxidizing at the surface, or a form of mould, living on the dead organic matter within the compost.

A gentle stirring of the surface with a small fork (or similar) should reduce the discolouration, and a watering with a copper-based fungicide used for damping off should check any fungal growth.