You say he married a Martha.
Are you aware of the William DIXON on the 1841 and 1851 censuses, c1776 Ramsden, in Shipton-Under-Wychwood on 1841 and Ramsden (Witney) in 1851, and buried in Shipton-Under-Wychwood 3 Feb 1856? He is married to a Mary (with children Emanuel, William and Caroline*). If he isn't the same person as the William who married your Martha then any birth entry you find for c1776 in the Ramsden area would well be for him instead.
(* also, it appears, a daughter Sarah who married in 1840, Emanuel is a witness)
(Further edit- Marriage William DIXON of Ramsden to Mary WHEELER of Ramsden 27th Mar 1815, Shipton-Under-Wychwood - so he cannot be the same person who married Martha unless he did so bigamously. I note the marriage to Martha says he is a widower but the marriage to Mary doesn't specify.)