He is the Sir Edward Barkham on p. 197 of the second edition of Faris' "Plantagenet Ancestry" who was Draper of London and member of the Virginia Company and who married Jane, dau. of John Crouch of Cornbury, Herts. They had a son Edward, 1st bart, who married Frances Berney in 1622.
He had a dau Susan who married Robert Walpole (d. 1663) of Houghton, probably Norfolk. (Burke's Extinct Peers, p. 566) Robt was gt-grandfather of Sir Robt Walpole KG, first Prime Minister of England c. 1722 and on retirement was made earl of Oxford.
_________________
From www.britishhistoryonline listing Alfred P Beavan’s “Aldermen of the City of London”:
February 28, 1611 [Faringdon Within Ward] Edward Barkham, Leatherseller S. 1611–2.
[Sworn same day] (fn. 39) [Nominated: G. Smythes, A. Prescott, II. Wollaston]
Removed to Cheap, April 17, 1621.
April 17, 1621 (
fn. 46) [Cheap Ward] Edward Barkham, Leatherseller (S. 1611–2.) M. 1621–2. From Farringdon Within. [Nominated: Alderman Sir F. Jones (Lord Mayor), A. Skinner, Richard Gresham (Goldsmith)] Transferred to the Drapers' Company, 1621. Knighted June 16, 1622; died January 15, 1631.
__________________