There is no doubt that this James Stone married a Charlotte Newman (his death certificate confrms this).
But, it might not actually be THIS Charlotte Newman in Wandsworth.
According to the Newman family tree researchers:
https://newman.one-name.net/getperson.php?personID=I40590&tree=...
The Charlotte Newman who got married to a James Stone in Wandsworth that day, was born in Bermondsey Surrey, remained in Surrey and had 5 children (all in Surrey) and died in Surrey.
I suspect this is not actually the same Charlotte Newman who married James Stone from Bath.