There are approximately 383,180 people named Brown in the UK. Approximately 6,065 out of every million people in the UK are named Brown.
"this ancient and prolific surname derives, from a pre 7th century Germanic and Anglo-Saxon word "brun" or the Olde Norse personal name "Bruni". Originally this name would probably have been a nationlistic or tribal nickname for a person with a brown complexion or hair, although it may also have referred to someone who habitually wore brown clothing, such as a monk or cleric." - The internet Surname database
Brown - dates back before 1066 and was often used as a nickname - P H Reaney & R M Wilson, Dictionary of English Surnames, Oxford University Press, 1995, page 68