Sorry but "grey mouldy" I don't think I can help with, but ants and minimal roots I can confirm both go together.
Ants will nibble the roots and leave your plants weakened. I have treated ants with powder in the past with limited success, but the biological ant-remover aka H2O seems to work pretty well. I've found the ants particularly successful in the greenhouse bed and under our bird bath - both places where there is not a lot of naturally occurring moisture. I shifted a load of ants from a greenhouse bed simply by watering it copiously and regularly. Funnily enough the sorry-looking spinach I was growing there really bucked up as a result. Beware waterlogging by over-watering and creating damp-induced problems though, vegetable-growing life is a delicate and rarely perfect balancing act!
Sad to say, I think the plants you have thrown away that the ants had been at might well have survived and thrived once the little beasties were sorted.