Hi
What we have is -
Some Bingham baptisms in Hatfield Broad Oak
Possibly starting with John in 1804. If you are logged in to FamilySearch you can see the BT - as explained by Rosie - here
https://www.familysearch.org/ark:/61903/3:1:9Q97-YSLX-V2K?i=1126&cat=494879But there are big gaps in these copies. Doesn't matter, because Nannyj has access to the parish register, and unfortunately there is no baptism of Mary.
But! - It seems that John Bingham had sisters Susannah and Mary who did not marry.
In Mary Binghams's will - very long one! - she asks to be interred in the family vault in the church yard of Hatfield Broad Oak.
Her burial
https://www.familysearch.org/ark:/61903/3:1:9Q97-YSLX-VRW?i=1405&cat=494879She then names
sister Elizabeth Hampton (widow) of Theydon Bois
sister Susannah Bingham (spinster) of Cheshunt
brother in law William Gentry of Abingdon, Berkshire (late of Hatfield BO)
nephew James Bingham
niece Mary wife of Henry Perry
niece Susannah wife of John Smith!
niece Charlotte wife of Richard Badcock (plus son William Gentry? Badcock)
Four children of Mary -
John Perry
James Bingham Perry
William Perry
Elizabeth Mary Perry
PERRY, JOHN mmn BINGHAM
1843 March Quarter in EDMONTON Volume 03 Page 157
PERRY, JAMES BINGHAM mmn BINGHAM
1845 March Quarter in EDMONTON Volume 03 Page 167
PERRY, WILLIAM mmn BINGHAM
1846 Dec Quarter in EDMONTON Volume 03 Page 136
PERRY, ELIZABETH MARY mmn BINGHAM
1849 March Quarter in EDMONTON Volume 03 Page 151
also
nephew John Bingham of Theydon Bois and his three children
nephew William Nicholls Bingham of Rayleigh and his five children
niece Ann Baines(?) of Black Lion Yard Whitechapel Middlesex, widow, and her five children
niece Elizabeth Bingham, spinster, now residing with me
nephew James William Gentry and his three children
That should be enough to be getting on with!
Not sure if this link will take you to page 559 of the book
https://books.google.co.uk/books?id=Nh0IAAAAQAAJ&pg=PA559&dq=#v=onepage&q&f=falseMight be easier to download the whole thing!
So although we don't have a baptism for Mary we do know who her parents were.
John