Happened to come across a few London Apprentice records for Beds Woodhams, which might help someone:
WOODHAM, Webb, son of Thomas, Sandy Beds, husbandman dec'd, to William Harris 20 Jun 1749, Carmens' Company
WOODHAM, John, son of Benning, Southill Beds, yeoman, to William Ringsted, 8 Dec 1757, Coachmakers' & Coach Harness Makers' Company
WOODHAM, Samuel, son of John, Sharnbrook, Beds, victualler, to George Summerlin, 4 Jan 1782, Paviours' Company
David