The main starch - indeed, the main source of calories - was cereal grain. The English cereals were wheat, barley, oats, and rye. These were consumed as bread, as beer, and as porridge/pottage/soup. Together, these provided about 75-80% of the calories, with poorer peasants probably eating more of their grain as porridge/pottage/soup.

These same grains fed most of Europe, with wheat and barley dominating in the south, and oats and rye in the north. The potato, adapted to the often-cold Andes, did well in often-cold northern Europe, and provided higher yields than grain, and therefore displaced grain as the staple food for many people. The potato similarly had a large impact in northern Asia and Tibet. (In parts of southern Europe, maize became the staple, again due to higher yields, especially on poor land.)

There were root vegetables in use before the potato: beets, turnips, radishes, carrots, parsnips, skirrets, salsify, burdock, and dandelions were the most important. Of these, the first 5 are still common enough on the English table. When grain was not available, either as the result of a poor season, or simply that the next grain crop was not yet ready to harvest, root vegetables could replace the calories normally provided by grain.

These root vegetables could also be eaten together with grain, such as added to pottage/soup (possibly with leafy greens and legumes as well). One example is this recipe for skirret fritters from the 15th century Boke of Nurture:

Take skirrets, parsnips and apples, and parboil them. Make a batter of flour and eggs. Cast ale, saffron and salt into it. Wet them in the batter and fry them in oil or in grease. Pour on almond milk and serve it forth.

This contains two root vegetables, skirret and parsnip, and grain in two forms, flour and ale. (Skirrets are root vegetables similar to salsify and parsnips, so you could try to make a modernised version using just parsnips instead of skirrets and parsnips, or something a little more different by using carrots and parsnips.)