Couch grass or twitch grass (Elymus repens)
Best treated with a weedkiller called Round Up once or twice in the spring you need to leave the area before digging over 6 weeks for the Round Up to work its way back into the roots of the Couch grass. Also apply on a mild sunny day if possible. The round up that hits the ground when applied is deactivated by soil bacteria and so its safe to use for your vegetable crops.
Another tip is the areas you are not going to use straight away I would cover over with black plastic silage sheeting from an agricultural merchants is best, Then in the spring plant your crops such as potatoes through the sheeting by cutting holes in it. You will find when the crop is removed the soil will be nice and clean with no couch grass.