Cereal cultivation in England/Wales/Ireland goes back definitely to the Neolithic, although the time frame for wide-scale forest clearing to make more room for agriculture is a little murkier. The climate in that era was much drier than today. Moorland and its cousin, peat bog, are significantly wetter than typical cropland suitable for cereal agriculture.

Now, medieval people were actually quite skilled at converting all sorts of land into arable turf! The Iberian interior and the Netherlands are examples of a sort of rudimentary, premodern geoengineering or human ecological engineering triumph, with developments in irrigation and draining to alter the land meeting developments in agricultural method to be more suitable for the land that existed.

So why not England?

Sheep.

With the population explosion in the later Middle Ages, England found or made its niche not so much as a producer and exporter of grain, but of wool. Sheep did well in the moorland. In Iberia, the other big locus of wool production, we have an avalanche of sources where ranchers and farmers complain about the damage that sheep do to their fields on the way to and from pasture. (The rancher-shepherds of the medieval Spanish kingdoms had immense legal protection.) This seems to have been somewhat less of a concern in England, though not absent. Moorland was super valuable for sheep pasturing. When lords gained the right of "enclosure" or the closing off of common property, they frequently seized moorland for their sheep--not just the more famous claiming of fields and forest.

Coincidentally I wanted to ask today why hilly parts of Britain like Snowdonia aren't forested. Have they been chopped down and then grazed enough to prevent regrowth?