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Eddie is descended from an Anthony MARKHAM who married Marcy/Mercy/Massey GIBBS on 18th February 1781 at Weston on the Green, Oxfordshire. Anthony died in Bucknell OXF in 1819 and was aged 68 on burial. This would give a date of birth of 1751/2. At his marriage, he was said to have been "of Bucknell" but there is no record in Bucknell of the MARKHAM name.
The only Anthony MARKHAM found so far that fits was baptised (according to the IGI) on 7th June 1752 at Tingewick, son of Anthony MARKHAM and Mary
Anthony MARKHAM and Mary appear to have had nine children from 1746 to 1764 in Tingewick but there is no record of a marriage around 1745.
Given the date of marriage, Anthony (snr) might have been born between 1720 and 1725 ... but there is no birth/baptism for an Anthony MARKHAM on the IGI in England, so Eddie is stuck ...