It would really help if we could start with what you do know (that we don't).
Are you descended from Robert the son? Who was his wife, and what child is your ancestor? (Or did he not marry/have children in England?)
Is there any findable record that might name his parent(s)? -- marriage certificate in England or Australia, death certificate in Australia ...? Or -- is that where the name Jane Hale has come from?
I'm wondering whether he was a son of Jane's from before her marriage to Robert Findlay (if there was a marriage). Robert Sr seems to have been considerably younger than her, and by 1851 she might have had a son who had already left home.
Since her sister was Mary Wood (I'm sure it says "Mar" for Mary Wood in 1861), the Elizabeth Wood visitor in the 1851 household was likely Jane's niece. Her birthplace was given as Romford. That could match a birth registered in June quarter 1842 in Romford. The birth certificate, if Mary was the mother, would give Mary's birth surname, which would presumably be Jane's as well. I wonder whether the sister is Mary Wood with husband John in Stapleford Tawney in 1841. Likely not, as she is also there in 1851 (and 1861), unless she was double-enumerated in 1951, which is possible.
There just was no Robert Findle/ay marriage in Essex before 1901. Either he and Jane married somewhere else, or they weren't married, I'd say. I don't imagine it's likely that she married and had a child in Scotland ...
Jane Findlay had the bad manners to die the year before age at death was recorded in the GRO index: December quarter 1865, in West Ham - that would seem to be her death, in any event.
I'd get hold of that death certificate to see whether it holds any clues.
There is no corresponding death for a Robert Findla/ey in Essex, or anywhere else in England that I can see.