Cream? Strict no-no for carbonara*. Bacon is a no-no either as pancetta isn't smoked. Save the cream for making mascarpone**.
I think the UK. uses the term "double cream" for whipping cream (~33% m.f.) and "single cream" (~18% MF).
* = been eating more than usual since I've started making my own pancetta from side belly pork.
** = which I also make because one supermarket insists on selling 2 x 1l container of whipping/heavy cream (33% milk fat) for about the same as 1 x 1l.