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I grew these a couple of years ago but when I came to harvest them the globes were completely covered in blackfly and full of ants. This put me right off and they were immediately dug up and put on the compost heap.

They seem to be a popular crop and I must admit I do like eating them. Was there a reason for the infestation or does this usually happen, is there anything that can be done to avoid this? Can anyone help please?

I think it comes down to 'bad luck'. Some years there is black fly everywhere and the ant were there to 'milk' the black aphids for their sugary 'poo' ::)
I can be off putting but you could have cut the heads...run them underwater and find that the heads would have been perfectly ok.
If you do few inspections now and then..and when there is possible first signs of the bleeders...just run your finger over them and give them 'loving stroke' ;)
If the population doesn get out of hand, spraying with soapy water (few drops of washing up liquid) with little cooking oil will kill them..or apropriate insectiside.
Most likely situation is that you don't get same problem again in hurry.
Couple of years ago I didn't have a single black fly about..that I could see. And last summer they were everywhere..making up for their absense ::)..one of those things.. ::)