In case it is of any help, my grandfather, Frank Henry Bloomfield b. 1901, worked with his cousin the Rev. Harry Bloomfield, to follow the Bloomfield family tree back to Sir William De Blomvyle c. 1222.
I understand there was a problem taking it back as far as Normandy to discover the very roots of Richard De Blonville; the French Authorities were apparently uncooperative.
I believe my mother, Barbara Bloomfield, may have a copy of the tree laying around, whilst the original will shortly be hanging on my wall. If any of you might wish to see a copy, I will see if I can arrange to have one sent to you... or you could always drop by to visit me in Suffolk... and bring a magnifying glass!