I'm not getting on very well with this one...
Starting with the 1851 Census you mention - just checking I'm on the right wavelength - Richard born 1818 Peckham was with wife Anna born 1812 Berkshire, and offspring Martha, 1844, Henry, 1849 and Elizabeth, 1851. Address Crown Street, Old Street Road, Shoreditch.
Looking for births for the offspring, James Henry Lee born Sep Q 1849 Bermondsey; Susannah ELizabeth Lee born Mar Q 1851 also Bermondsey. Mother's maiden name - Moorcroft. The only birth for Martha to come up is 1844 Kennington, mother Goddard, which doesn't seem right.
Then looking for baptisms for them: James Henry Lee baptised 23 Sep 1849 Horsleydown, parents Charles Lee and Susannah ELizabeth; Susannah Elizabeth Lee baptised 16 Mar 1851 Horsleydown ditto names of parents. There was a Martha baptised 13 Jul 1845 Kennington, parents Charles Lee and Priscilla, but this doesn't fit in too well.
A Charles Lee married Sarah Elizabeth Moorcroft 23 Aug 1843 Lambeth, their fathers were John Lee and George Moorcroft.
Looking for a baptism for Charles:
Charles Angelo Lee on 14 Nov 1818 St James, Westminster, parents John Lee and Mary. Abode Angel Court, John was a Breeches maker.
Can't find Richard in 1841.