I have found records that say Charlotte Elizabeth Varley B:1819 was in court in August 1847 suspected of infanticide.
I know that she was found not guilty however I cannot find information on the birth of a male child other than Henry William Gamble B:1841 who didn't die until much later.
The court papers say "The particulars of this case were unfit for publication; but from the evidence of the surgeon it appeared that the death might have been occasioned without any criminal act on the part of the prisoner."
I have tried looking for any information in the papers, the GRO, Ancestry and FindMyPast.