When Globe Artichokes are flowering they are such a valuable food source for bees and all sorts of other insects, so we’d encourage you not to cut them back too early or too vigorously until they have finished flowering. You don’t actually have to cut them back at all, but we find the plants grow back healthy and strong the following year when we do cut them back.
Towards the end of August, have a look at your plants – you can happily cut back the stalks that have already flowered, and any dead/dying foliage. You’ll probably see newer growth appearing at the base of the plant – be sure to leave this. Any remaining flowering stalks can then be cut back to the ground once they have finished flowering.