These insects suck the sap of the plants, and therefore tend to congregate on the juiciest, most tender bits - that's to say the tips of the plants.
Because of this habit, it is usually possible to limit (I won't say "eradicate", that would be too optimistic!) an infestation before it gets too bad, by cutting off the top few inches of each plant, like this:-
The tips of Broad Bean plants are edible and supposedly make a tasty vegetable, sometimes used in stir-fries etc, but the trouble is who would want to eat something that is covered in Blackfly?? You would have to wash them very carefully...
Incidentally, cutting off the tips of the plants is also alleged to increase the yield, because the plant puts more energy into pods instead of leaves, though I can't vouch for this myself.
Of course, there are other ways of dealing with Blackfly too, for instance by spraying with horticutural soap solution, or even with proprietary insecticides. I have found that using a hose to spray a fine jet of water at the plants can usually remove most of the Blackfly - though this is a task that needs to be repeated every couple of days because they reproduce very rapidly!
I think (hope) I will win the battle this year, because the Blackfly are only just moving in, but the development of the bean pods is already well advanced...
Wish me luck!
