You probably have most of this, which I guess led you to the cohabiting assumption?
Abode Fore St. John a Labourer.
Eliza Roberts 4 Oct 1818 All Saints, Edmonton Enfield John,Ann
Abode Fore St. John a Gardener.
Elizabeth Robarts 22 Apr 1821 All Saints, Edmonton Enfield John,Ann
Parish Register.
John Roberts Married 5 Sep 1824 St Andrew, Enfield Anne Bird
Both widowed of the parish, signed X, witnesses John & Mary Head.
Typed Transcript
John Roberts Married 5 Sep 1824 St Andrew, Enfield Ann
Parish Register.
John Bird Married 14 Nov 1802 All Saints, Edmonton Ann Head
Both single otp, signed X, witnesses John Head & Joseph Wood
Mary Ann age 38 on 1851 census so born about 1813.
Mary Ann Bird 17 Apr 1814 All Saints, Edmonton Enfield John,Ann
Abode Fore St. John a Soldier, below also notes John a Soldier
William Bird Baptism 18 Oct 1812 All Saints, Edmonton, Enfield, Middlesex John,Ann
No burial in Edmonton for John or William before 1824?
As John Bird was still a soldier in 1814, I wonder if he was still active, Waterloo 1815?
Colin