There are greenfly and whitefly in the picture, both naughties. The soil looks pretty manky in the picture, badly drained and stale, is it peat? I would suggest that you break up the surface crust to allow air in and keep the surface loose. Next year use a more freely draining compost with more grit in it.

Greenflies frequently fall to the soil, but normally don't survive there long--centipedes and carnivorous beetles usually get 'em. I mainly see old greenfly skins in the picture. The juveniles shed them as they grow, so they build up fast under a thick infestation. The main problem is above on the leaves. I agree with Bulba's comments on the soil, though. Grit and/or perlite recommended for the next crop.

Thanks very much. I thought that was the case. The plants are planted in large polystyrene boxes. I made holes in the bottom and put in pebbles for drainage before filling them with multi-purpose compost. Is there something I should spray the plants with--such as a mixture of water and washing up liquid--to try to kill the green fly?

I would use a diluted organic washing up fluid, or a commercially available insecticidal soap. Be sure to spray thoroughly, and frequently. They will only kill the aphids that you spray directly, and they have no residual action.