This could be powdery mildew. The coating of powdery white fungal spores tends to appear under humid conditions at this time of the year, and is particularly seen when the plants are dry at their roots. Although it is rarely fatal on box plants, it may cause them to drop some leaves and can certainly look unsightly.To treat it, spray the plants with a systemic fungicide on a dry, overcast day. There are lots of fungicides available in garden centres, but you should always check the manufacturers instructions first.
To prevent further outbreaks we would suggest keeping your plants well watered (try to water them at the roots and not from above as this is likely to spread the spores). Cut out any heavily infected shoots and burn them. In autumn, remember to clear any neighbouring plant debris away from the area as this is likely to harbour over-wintering mildew spores. Finally, try to maintain good air circulation around the plants by keeping them spaced well apart.