I think you need to complete the census details and you will answer your own question!
Doesn't matter whose site you look at the census image on, unless you are looking at the index when errors creep in.
In 1851
Liberty of The Rolls, St Clement Danes
William Baker head marr 53 Collector steam boat co b Clerkenwell
Jane Baker wife 44 b Hampshire Blackwater (I can understand how it might have been transcribed as Cambridgeshire)
William Baker son 17 app carpenter b Holborn
Mary Ann Baker dau 23 fancy stationer b Holborn
Jane Eliza Baker dau 21 fancy stationer b Holborn
Elizabeth Sarah Baker dau 19 fancy stationer b Holborn
George Charles Baker son 13 scholar b Westminster
Alice Martha Baker dau 7 b City
Helen Baker dau 3 b City
The 1841 family you mention
William Baker 35 tobacconist
Jane Baker 25?
Mary Baker 3
Janie Baker 1
All born in Middlesex
In 1851
119 Fetter Lane, St Dunstan in the West, London
William Baker head marr 43 Money taker to steam boats b Clerkenwell
Jane Baker wife 33 b Hampshire
Louisa Baker dau 14 b St Clements
Mary Ann Baker dau 13 b St Clements
Jane Baker dau 11 b St Andrews Holborn
William Baker son 7 b St Andrews Holborn
George Baker son 3 b St Andrews Holborn
1841 looks as though it's the same family. But the presence of Louisa age 14 in 1851 complicates matters as it makes a Dec 1838 marriage in Richmond Surrey more unlikely. But we can speculate until the cows come home. It will take the birth cert of one of the children to prove it one way or the other.
Births/baptisms of most of the children are on the IGI
David
