BIRTH cert would give you the father's name and occupation, and the mother's maiden name.
But the MARRIAGE cert would give this information plus their ages and their fathers' names which is extremely useful in tracing them, and the father's name could be a reference point for the birth certificate. (So you could eliminate any with the wrong father)
You have the reference for the marriage cert.
Order from the General Register Office (GRO) cost £7
http://www.gro.gov.uk/gro/content/certificates/reference
Marriages Sep 1840 (>99%)
Hodges Sarah Lambeth 4 238
Jennings John Lambeth view
LYON James Lambeth 4 238
Nicholls Joseph Lambeth 4 238
PENICUD Amelia Lambeth 4 238 <<<<<<<<<
WALTERS Ann Lambeth 4 238
WARREN Henry Lambeth 4 238 <<<<<<<<<
WILLMOT Thirza Letford Lambeth 4 23
Do you have a reference number for the birth cert? (for James William b1845 - where was he born - can't see him on freebmd.)
The child born 1848 has a VERY similar middle name to Amelia's maiden name, do I am inclined to think it may be the correct marriage
Births Sep 1848 (>99%)
Warren Edward Penioud Languin Stourbridge 18 518
If you are certain of the children it may be worth getting at least one of their birth certs, just to confim the mother's maiden name (mmn).