If you don't prime it you'll have flat beer. For a bitter I'd say maybe 3 oz to 3.5 oz of corn sugar for a 5 gallon batch to fit the carbonation level of the style.
Isn't Boddingtons considered a bitter? The recipe I followed for that called for 3/8 cup packed dark brown sugar. I'm not exactly sure why it called for this, rather than corn sugar. I suppose I'll find out how it tastes in a few weeks.