Is communication with cabin crew or ATC included in emergency checklists? In a serious but non-catastrophic situation on a commercial flight (for example, a single engine failure on an A320), I understand that the pilots will follow a standard checklist (from the QRH) to put the aircraft into a safe condition.

My question is - will such a checklist generally include an explicit item to inform ATC, the cabin crew, and/or the passengers, or is this generally assumed to be done as a "standard procedure"?  If it is usually on the checklist, would it always come at the end, or are there situations where ATC might need to know about the incident as soon as possible?
In the case of A320, yes it does. Here’s an example of the emergency procedure for ditching. Note there are four instances where it tells the pilot to communicate with the cabin.