de Vere and de Mandeville
There is a similarity in the sheilds of the two families. Under normal heraldic norms this would indicate a connection between the families.
J. H. Round in his book "Geoffrey de Mandeville - A Study of the Anarchy"
The de Veres and Belchamp Walter
The generally accepted theory relating to the history of Belchamp Walter the de Vere's are the "owners" at the time of the General Survey.
I am not sure what the (still officially held by the de Veres) means and even if it is a true statement of fact. I would suggest that it is a gross over simplification of the history in the period between the 11th century and 1611.
Mandeville, Normandy
The connection to William the Conqueror and the de Mandeville family is starting to reveal itself. In the attempt to work out why the de Veres got to be so influencial and where they are from led me to postulate that the de Mandevilles were originally from Mandville in Normandy.
The association of a modern place name with an individual from history is problematic.