I have a lot of information from the 1841/51/61 censuses via Ancestry.co.uk including birth year range of 1793-98 and birth place as mentioned; an 1863 death record from BMD index via Ancestry; children's christenings from IGI (at St Matthew Bethnal Green) via FamilySearch.org, and a possible marriage on Pallot's Marriage Register. This 1816 marriage to Ann Allen is confirmed in Hackney Church's records at the London Metropolitan Archives (LMA) but I fear this is another branch of the family. I also searched St Matthew's, St Dunstan's and Hackney Church's records at the LMA for a 1790s birth for JB but to no avail.