You probably have already seen these but it does'nt help much...
http://www.genealogy.com/forum/surnames/topics/gillam/494/http://www.genealogy.com/forum/surnames/topics/gillam/462/"My Delamonts in Somerset also have an alias that was used for more than two
centuries. Thus we have Delamont (Daleymount etc etc); Delamont alias Gilham;
Gilham alias Delamont; Gilham (Gillam etc); and even Gillingham".
"While I and my cousins who are researching this line cannot yet prove our
descent from Nicholas Delamont who was made a denizen of England in 1544, it
is likely that we are, and that one of the early family members was called
William, or Guillaume in French, hence the corruption to Gilham."