You can spray with a herbicide, then cover with black plastic over winter and dig + manure as you go along, or even better, get a couple of fattening pigs (if you are allowed, you will need a holding number), give them small area (and move on after they have thrashed it), they will clear it for you and manure, then plant potatoes or anything else that needs lots of manure next year.
What we did when we first started, was built raised beds, turned over the clods of grass etc, added manure and lots of soil at the top. Worked fine. We started with a couple of beds, (but had a complete layout planned), and have added on beds each year.