Some maps of medieval England show portions of land as "swamp or alluvium". Here is an example. Does that mean that that land was unusable or uninhabitable? What happened to that land since then? Man-made efforts to drain/reclaim that land, I assume?
These areas were not necessarily unusable or uninhabitable but were/are definitely swampland.
The one in your map that is in the southwest (between Edington and Exeter) is the Somerset Levels. The name 'Somerset' may actually derive from the fact that this area is near the sea and/or only usable in the summer (due to flooding). People have been living in the area for thousands of years, especially on the natural islands like Glastonbury (which has sometimes been identified as Avalon of the King Arthur mythos).
Much of the land has been drained since then - but not all of it in modern times. Drainage of the Somerset Levels started before the Norman invasion, mainly by the monasteries in the area, though more progress was made during and after the Second World War.
Much the same could be said of The Fens (the marshy region north of Cambridge on your map) and the North York Moors (east of York). All of them are swamplands that have been used and engineered for thousands of years.
