"Forest" in medieval england wasn't dense woodland. It was land managed for hunting, primarily deer. There were villages and farmland in the forst area, but Forest Law applied. Pretty much, you'd have the normal English trees: oak, ash, elm, birch, and a lot of others. The deer would probably lead to fairly open woodland that was short of ground cover. The Woodland Playsets come close to that look. Modern Sherwood Forest is mostly on lighter, sandy, soil, which has some effect on which trees thrive. Places like the Dukeries, to the north, are relatively modern managed landscapes, of the sort associated with Capability Brown.