An interesting challenge to start so late. Even a month ago would have been much better, I am unsure that you can sow wheat in June and have a harvest though perhaps a long Spanish autumn makes it possible. Most wheat in Britain is forming its heads already.
Unless you have access to much compost, and being unable to use polythene, I would dig: to bury weeds and enable your immediate sowings. Firm the soil after digging to conserve moisture.
Meanwhile I would sow corn and squash and beans in pots/trays of compost, to plant in about 3 weeks, when you will have prepared the ground.
