Thank you all very much for your responses so far. They are very greatly appreciated.
According to family lore (which we all know is not authoritative), the father was definitely Henry Elliott Smith, and his son, also Henry Elliott, definitely married Isabella Brabazon. We have proof of this much at least. (She was a member of the extended family of the Earl of Meath). The marriage date of 1867 is in the right range for Henry Elliott (junior), as the first child was born in 1868, but the wife's name was definitely not Browne. The children listed for Henry and Isabella Browne share some similarities, but are not correct for my Henry Elliott (junior) and Isabella Anne, which were William 1868, Ida 1870, Florence 1872, Lily 1876 and John 1878. There is ample documentary evidence (captioned photos, correspondence etc) to confirm the name, so that family is definitely not my family.
The baptismal date of 26 December 1841 for Henry Elliott (junior) could be right (we thought about 1842), but again we have the problem of the father's name. The burial date of 1847 would be correct for our Henry's (junior) father, but the name and occupation appear incorrect. While I cannot definitely rule out the father being William, I do not believe that the occupation could possibly be correct.
I started this search thinking that Henry Elliott Smith must be an uncommon name, but apparently I was wrong! Anyway, thank you all again for your input so far, but I believe that the people found so far are from a different family.
Terry