Background information on this era is very opaque; record keeping was almost nil, which is why the Domesday Book of 1086 is so notable. It was a huge survey of landholders, their landholdings, and their value, primarily for paying of royal dues and taxes. Despite its ambitious scope, it remained an incomplete survey of England. Not only were important cities like London excluded, but only heads of households were counted, i.e. potential taxpayers. Clergy, women, children, artisans, merchants, serfs and the rest were excluded, and we don't have an accurate householder:population ratio available beyond speculation.

You can actually access the book here http://www.domesdaymap.co.uk/book/kent/01/

William's force at the Battle of Hastings is also uncertain. You see laughable estimates as high as 1,200,000 by Guy of Amiens in Carmen de Hastingae Proelio. Of modern historians, Peter Marren puts it at 7-8000 men, 1-2000 cavalry, while M.K. Lawson puts it at 10-12,000 men. I think it's reasonable to estimate anywhere from 2,000-3,000 people in the baggage train and camp followers considering typical armies and the lesser amount there would be for a quick battle after a landing than a long overland campaign. William's army did have, and rely on, horses, which always increases the logistics involved.

In terms of post-Hastings settlement, we know the English Anglo-Saxon aristocracy was basically replaced completely by William's Norman lords. Where castles did not exist to take over, William went on a massive castle building campaign. England had a sufficient population at the time to be relatively prosperous, with a few cities even capable of supporting 10-20,000 people. Richard Huscroft suggests 8,000 Normans settled after the battle, presumably along with many of the surviving knights, squires, and sergeants. Most modern estimates for England's population at the time run from 1.25-2 million, considerably less than the upwards of 6 million during its time as the Roman colony of Brittania.

If you're wondering for reasons of language and culture, the Norman lords were fairly estranged from the populace until Henry II and beyond, only assimilating very gradually over hundreds of years. A big reason for the eventual fusion of French and Old English came from Norman patronage of literate Anglo-Saxons, that is to say, the clergy.

Fun Facts: For those not in the know, "Normans" are derived from Normandy, where William had lands and English kings would have lands from along with Poitou and other regions for the next 140 years, and both are derived from "Northmen." English kings would speak French, and very few old or Middle English, for hundreds of years, and conduct the court in Latin. Other Normans like Robert and Roger Guiscard conquered southern Italy over several decades and became a major thorn in the Byzantine/Eastern Roman Empire's side.

Huscroft, Richard. The Norman Conquest: A New Introduction. Boston: Routledge, 2009.

Lawson, M.K. The Battle of Hastings 1066, New York: Tempus Publishers, 2002.

Marren, Peter. 1066: The Battles of York, Stamford Bridge and Hastings. London: Pen and Sword, 2004.