Do you really have to plough? The reason I live near what was set a side, the last time it was harvested for barley it was left, not sprayed or ploughed. Over a season it sowed its self with native grasses which until three years ago it was just left and then with the hay shortage its been sprayed in spring and then cut for hay and they have really good yields.
I would just harrow it and get someone to over sow with grass mix, this will give you a good mix of grasses some of which will be naturally suited to your land. It means if you do this in spring that you can put livestock on it May or June. Unless you want rye grass for cattle this will be far better grazing and better for wildlife. I have done this and been very pleased with the results my ponies had grass until December and it was still growing when I brought them in because of the wet. Grass seed is not .cheap.