His b/c would give you his mother’s name
Brierley Hill is in the registration district of Stourbridge
closest birth entries I could see FreeBMD
CARTWRIGHT David Henry Jun 1862 Stourbridge 6c 220
CARTWRIGHT David Jun 1861 Stourbridge 6c 244
CARTWRIGHT David Dec 1863 Stourbridge 6c 181
There's this marriage entry
Jun 1861 Stourbridge 6c 210
CARTWRIGHT Samuel
Female names on same page
Ann CARNNIDGE
Lucy WATSON
There are a few death entries in Stourbridge for a Samuel Cartwright see FreeBMD
http://www.freebmd.org.uk/1871 David Cartwright age 10 Kingswinford inmate
https://familysearch.org/ark:/61903/1:1:V5R1-35MAmendedWas just going to post marriage info. David Cartwright to Sarah Beddall which probably relates to this David - see Rosie has beaten me too it

There’s this 1871 entry
https://familysearch.org/ark:/61903/1:1:V5TZ-5SHDavid Cartwright grandson age 10 Kingswinford