I've just found this on a gardening site to add to the answers you have already. "These little devils reproduce themselves from underground bulbs and then from seeds later in the season. It's the little bulblets that make them so hard to deal with because they can be as deep as eight to ten inches underground.
The earth friendly way to deal with wild garlic is just to dig up the clumps. You see, if you try to pull them up you'll just tear off the tops and they'll be back to haunt you.
Now to make your job easier in removing these, soak the area you are going to work in the night before. When you make your cut with the shovel, push it as deep into the ground as you can close to the garlic".