I believe your Susannah would have been a cousin to my great grandfather,William Henry Frostick.I show his father, also William Henry, and James to be brothers, the children of John Frostick & Lydia Lansdale.
John & Lydia married in 1782 and lived in the City of London. There were several children born to them, but the only ones I have been able to follow up on are (Samuel) James & William Henry. They lived for many years on Upper Thames Street in the city and both were christened at St. Martin-Vintry Church.
This was later torn down and the family attended St. James Garlickhithe(church is still there today) and the first children of James & Sarah were christened there. (Some church records show him as Samuel James and others as James, but at the same address with the same wife)
Some time during the mid 1820's James and Sarah moved to the south side of the river and lived in Lambeth and then Bermondsey. Susannah was a common name in the family, as the brothers had a sister by that name and both William Henry and James named a daughter Susannah.
I am still researching the family, hoping to find out more about John & Lydia. It gets harder the further back you go.!!
I hope you find this information interesting and helpful. Let me know if you have any questions.