Allium Invasion!
Although one of it's common names is wild garlic, it should not be confused with our native wild garlic garlic or Ransoms (Allium ursinum).
Allium triquetrum or three cornered leek is an invasive species from the Medeteranium region, and is currently finding the Uk climate to it's liking.
As you well know, it is a tiresome weed to eradicate, but on an up note the plant is edible it can be eaten cooked, pickled or added to salads.
I would say it's probably best to harvest what you dig out and hopefully enjoy it, rather than throw it out, which also helps it to spread.