Castle Street runs behind where this old Workhouse was.
"Castle Street, Edgeley", as it's more commonly known in Stockport, doesn't actually run past, adjacent to or behind the site of the workhouse and I suggest that you check on one of the easily available mapping programmes to check the relationship.
Castle Street is the main shopping street for the Edgeley district - in now partially pedestrianised - whereas the workhouse/St Thomas Hospital site is on Shaw Heath (the road, not the district from where it derives its name). There is a distance of around 200 yards and the main Manchester/London railway line between the two.