Be very careful with Transpose!
If you add a line:
x = Application.Transpose(Date_Set)
to your code and examine/compare Date_Set and x in the Locals pane you will see that while Date_Set contains values of type Date, x contains values of type String. When strings are written to the sheet you're hoping that whichever locale you're using Excel in the date format is the same as the strings in x, because Excel tries to be helpful and converts a string that looks like a date, into a real date but will get it wrong if the month/day position is different as in US/UK dates.
You can avoid Transpose by changing:
ReDim Date_Set(1 To No_Data_Rows * No_Data_Columns)
to:
ReDim Date_Set(1 To No_Data_Rows * No_Data_Columns, 1 To 1)
and changing:
Date_Set(c) = Cell
to:
Date_Set(c, 1) = Cell
and changing:
Sheets("Converted_Data").Cells(5, 4).Resize(UBound(Date_Set)).Value = Application.Transpose(Date_Set)
to:
Sheets("Converted_Data").Cells(5, 4).Resize(UBound(Date_Set)).Value = Date_Set