The figures are unknown but were heavy for the Normans and disastrous for the Saxons.
Follow-up: It was some time before Saxon England acknowledged William as king. William was forced to march to the West and cross the Thames at Wallingford in Oxfordshire before circling round from the North and capturing London, devastating the countryside as he marched. The Tower of London was the first of the castles William built to dominate and subjugate England. William was finally crowned in Westminster Abbey on Christmas Day 1066 by the Saxon Archbishop, Aldred of York.
In March 1067 William returned to Normandy, leaving Odo, Bishop of Bayeux, to continue the process of building castles and subjugating the population. William only returned to England on four further occasions. William the Conqueror died following the capture of Mantes in 1087, leaving England to be ruled by William II and Normandy by his eldest son Robert.
Probably only 20,000 Normans and other Frenchmen came to England as a result of the Conquest. Nevertheless the Saxon country was transformed, French becoming the language of administration and government and the Conqueror’s followers displacing the native nobility. The Saxons lamented their lost freedom for two centuries while England now looked across the Channel for cultural and political inspiration.
Conquest in France remained the obsession of the Frankish kings of England until the 16th Century. French names predominated among the nobility and the military classes; doubtless the Montgomery leading the British armies in the Second World War was a descendant of the Roger de Montgomerie who fought for the Conqueror.