Found this Sarah Brown and family on the 1851 census.
Civil parish Hammersmith
Registration district Kensington
Sub reg district Brompton
8 New Street
Henry Brown head age 38 occ bricklayer/labourer born Wiltshire
Mary wife age 42 occ charwoman born Urchfont Wiltshire
Jonathon son age 16 occ bricklayer/labourer born Urchfont Wiltshire
Henry son age 7 born Hammersmith Middx
Sarah dau age 2 born Hammersmith Middx
(not to sure about the place in Wilts where Henry was born)
I havnt looked through all the 1851 census for Sarah Brown born Hammersmith but came across the above. Will have another look through
As Sarah Brown is a common name its hard to determine which one she is on the birth register. The marriage certificate for William and Sarah will give fathers names and occupations.
You can apply for bmd certificates at £7.00 each by using the the link below.
http://www.gro.gov.uk/gro/content/certificates/