Another search of 1837Online revealed several possible Charles
Browns in the Hertfordshire/Bedfordshire area. Previous investigations showed that
Charles was born in Little Berkhamsted (or at least, was christened there in 1863, and gives this as his birthplace in several censuses). Some possibilities:
St Neots 3b 306 Apr-Jun 1862
Hitchin 3a 249 Apr-Jun 1862 (I tried ordering that one and it wasn't the right Charles)
Luton 3b 407 Jul-Sep 1862
St Neots 3b 263 Jul-Sep 1862
Bedford 3b 350 Jan-Mar 1863
Hitchin 3a 254 Jan-Mar 1863Luton 3b 472 Jan-Mar 1863
The second Hitchin one seems most likely, so I'll try ordering that one.
(UPDATE: I finally found the certificate for an unnamed male child BROWN, father Benjamin, in 1862).