An alternative family for Henry:-
1841 HO107/1049/5/30/13
(with grandparents Henry and Catherine)
1841 HO107/1061/8/49/17
(his father Henry,a constable at the Surrey Theatre).
1851 HO107/1565/421/6
Three generations together.Henry given as born 1840,Christchurch,Surrey
I think this would make him Henry James Peckham June qtr 1840 St.Saviour vol 4 page 438
1861 RG09/334/92/39
Henry's(1840) father and grandmother together.
No mother for Henry(1840) appears in any of these censuses.GRO info would give her maiden name as Kean.
Regards
Roger