Hello Carol
This is all very intriguing, so I've had another hunt, starting with Gardener's find of a Charles and George in 1851 (HO107/2047 Folio 823 Page 18) I originally was pretty positive that Charles was 13, but on looking again there are some other marks around the age column so it is just possible that Charles actually
is down as 3 not 13 and the apparent preceding figure is one of those marks. What do other people think? It would certainly match otherwise, as George is down as a widower. (Sorry, Gardener

)
Following on from that, there's a death registered in the right district, MAR 1850 Bromsgrove 18 191 for a Harriet
Wolding 
who might just possibly be the missing Mum for Charles.
I did wonder whether the family George and Charles are with in 1851 might just possibly be relatives of Harriets (not George's since his place of birth is down as not known). Just in case that's a possibility, the full entry is-
78 London Street, AlvechurchSamuel Bayliss - Head- Mar -38 - Ag Lab - Worcestershire, Alvechurch
Eliza Bayliss - Wife - Mar - 29 - Needlemaker ( Hard Str
tner - Worcestershire, Tardbigge
Charles Bayliss - Son - - 1 - - Worcestershire, Alvechurch
George Walden - Lodger - Widr - 35 - Ag Lab - N.K.
Charles Walden - Lodger- -?3 - - Worcestershire, Alvechurch
Angela