There's some possibles as 'Stotesbury' in St. Leonard Shoreditch in 1841, and others by that spelling scattered around; do you have some first names/dates to go with your Stutsburys, Vanessa?
This is the St. Leonard's Shoreditch family, at Catherine Street:
Matthew Stotesbury, 50, carpenter, b. Ireland
Charles, 20, carpenter, b. London
Matthew, 13, b. London
Hanah, 9, b. London