Last year, my first year on this allotment, was facing the same problems. The first bed I made was a lasagne bed. I had some big branches which I made the bed out of and then put cardboard on the bottom over the weeds, a good thick layer, then filled the bed with all the waste I could lay my hands on, just like a compost heap. I put a couple of inches of compost on top. The main difficulty would be the slugs, but I did not experience a huge increase in slugs here compared to the rest of the plot. This bed has grown perpetual spinach, chard, beetroot, spring onions and then sprouting broccoli and kale. Have added nothing more and there is now 6 inches of compost without adding any more to the bed and very few weeds.
I also made 2 hugel mounds. Dug a trench and put in logs and branches, horse manure, straw, topped off with soil and compost. The theory is it will be self watering and feeding for many years. Again they were planted in the first year and grew romanesco caulis, parsley, sweet potato (not great yields!)tomatoes, cucamelons, cucumbers,and squash. I started in April too.
Just a couple of ideas, if they are new to you there’s lots of info on the web.