You did not mention this in your post, but are you aware that John was a Catholic? At least, he baptised his children Catholic, and he and his wife Sarah are down as such on their workhouse admission record.
His sons Edwin and Alfred were baptised at the Catholic church of St. Mary Moorfields. A useful part of Catholic baptisms is that they provide the names of the sponsors (i.e. godparents), who are often relatives of the parents. In my experience (my father is Irish so I've seen a lot of Catholic baptism records), the godparents were often siblings or siblings-in-law to the parents, or occasionally cousins.
Edwin's godparents were John Erley and Margaret Derry, whilst Alfred's were John Earley and Ann McCarthy. Given that John is unlikely to have had a brother with the same name (although not impossible), could this perhaps be John's father? I don't usually see grandfathers as godparents, though.
Interestingly, there appears to have been a third son born to John and Sarah, many years after their first two. In 1872, a two-month-old child, Arthur William Earley, was baptised to John Earley and Sarah Ann Earley, formerly Bruce. The godparents were Edwin (unusual for someone to be made godparent to their own brother, but there was a large age gap) and Johanna Earley. Sadly, Arthur died in infancy.
Queenie 
Firstly a big thank you for responding to my request for help and an apology for the delay in responding to your post.
You did not mention this in your post, but are you aware that John was a Catholic? At least, he baptised his children Catholic, and he and his wife Sarah are down as such on their workhouse admission record.Yes all of my Paternal and Maternal lines are Catholic.
Its almost certain that at some point the Early’s or Earley’s came over from Ireland looking for work in the London or Liverpool Docks .
Edwin's godparents were John Erley and Margaret Derry, whilst Alfred's were John Earley and Ann McCarthy. Given that John is unlikely to have had a brother with the same name (although not impossible), could this perhaps be John's father?Now this is very interesting as it is thefirst record that I have seen in connection with my Earlys that mentions an Irish spelling of Early ie Erly.
I have just discovered an extensive research on the Irish History of the name Early by a chap called Stephen whose Surname I have been unable to discover. I hope that it is acceptable to post his URL on here ?
https://shorturl.at/RZLO6Unfortunately I do not have access to online Baptism records,.. other than through one of the Geneology sites which sadly I can no longer afford .
On John and Sarah’s Marriage certificate, John’s Father is noted as John Early, but not as a witness.? I think it is therefore reasonable to assume that perhaps he could not present at their Marriage and might posssibly have been dead , abroad, or just unable to attend for some other reason due to work or health etc.
Interestingly, there appears to have been a third son born to John and Sarah, many years after their first two. In 1872, a two-month-old child, Arthur William Earley, was baptised to John Earley and Sarah Ann Earley, formerly Bruce. The godparents were Edwin (unusual for someone to be made godparent to their own brother, but there was a large age gap) and Johanna Earley. Sadly, Arthur died in infancy yes I have previously found 2x records of a Birth of a child named Alfred, one in 1849 and another in 1851 but no further record of either. i had not come across the late birth of William though so thank you for that source
At the moment I just don’t see a way of progressing this search further, which is why I am hoping for some experienced advice and suggestions .
