We'll be on a BA flight. Is 2 hours enough time to check in? Our flight leaves at 3 pm.
It should be. It is consider a domestic flight but FCO can get pretty wild by that time of day. Lots of local flights departing. I would not cut it any closer than that. And there is a 45 min cut off that has been firmly enforced in the past.
As the UK is not in the Schengen Zone you will have to go through passport control as well as security. We allow 2 hours when returning to the UK as per the usual BA advice.