First you have to note that you are talking of agrarian communities.
Next, you need to look at what land was available for farming at the time - the reason for this is that today a great deal more land is in use than was the case.
Take, for example, Towton Moor in West Yorkshire, which was the scene of the bloodiest battle ever fought in England. Today is is gently rolling farmland, there are no marshes, and the small water course - Cock Beck, is just that, a stream.
On the day of the battle it was quite differant, it truly was a moor, bleak, marshy, Cock Beck was in flood, it certainly was not farmland.
Large areas of England were not used for farming at all, it was forested such as the huge Knaresborough forest that ran pretty much all the way through Yorkshire.
The settlements were obviously much smaller, and were crowded into the areas of best farmland.In plenty of places these grew and seperate villages became suburbs of the modern cities.
Here is a link to a map of Wakefield Manor.
The area around Wakefield to the South East is fairly flat and good farmland, and if you look to the north east, this is just stretching to the edge of modern day Leeds, this is reasonably gentle land.
These settlements appear to be about three miles apart, though many are less than that.
The problem with these settlements are that they are pretty much still in use, that’s because they were built with far better materials and have survived, plus they were in the best locations,whereas medieval villages would move around quite a lot.
The houses were generally speaking very basic, and didn’t last more than a couple of generations, and villages would often be entirely rebuilt a few hundred yards from the old one.
You can expect that the true village density was very much higher, but that most villages have simply dissappeared over time.
Villages were abandoned and their remains have often been lost, ploughed into the fields etc, al that remains is pottery shards, or just a few marks in the soil patterns that can only be picked up in certain lighting conditions when the sun is low.
There are at least 3000 deserted villages in England, that number is probably a huge underestimate, as large projects, such as village bypasses which are often on very old farmland, reveal more sites - this has caused a revison for the population density of England.
The Domesday book gives us a good idea, but it depends upon which period you wish to discuss, because large areas of Northern England were partly depopulated in the genocide practiced by William the Conquerer in 1086, so the Domesdays records of that time will tend to show a much lower than normal population, at around 10 persons per square mile.
You can roll on say 200 years and the population increases somewhat.
Things such as Black Death did cause a reduction in populations, but the evidence is that villages that were abandoned, as the remaining survivors consolidated into other surviving communities, were largely recolonised.
There were many reasons for village abandonment, one of the mains ones was eviction for sheep.
Wharram Percy, village in the Yorkshire Wolds was considered to be a fair sized village of around 150 people, so if you take that as a middling sized village, and a national population in the 1400’s of perhaps 4 millions, you get a rough idea of just how many villages there were. I’ve been to this village during the archealogical excavation season over the years, and nowadays its a very quiet place, its probably at its lowest population during this century than it ever has been in the previous thousand years.
Farm sizes have increased dramatically, and th enumber of farms has fallen as farms have beome more mechanised. The number of workers has fallen so much that villages shrunk to maybe just one or two houses, and are no longer considered villages as such.
If you go into an old agriculteral area such as the Vale of York, you can’t go much more than two or three miles without coming across a village, it reasonable to xpect that when the rural population was larger, there would have been villages perhaps less than a mile apart.
If you go into the more marginal areas, such as toward the moor uplands, you’ll find that villages are further apart, these would be sheep farming, which didn’t require as much labour and villages would be further apart, perhaps three miles or so.