Hi moondog
Welcome to the BA forum!
Given it is Christmas Day, there are less flights operating and sadly BA only have 1 direct LHR-FCO flight on Dec 25th which is currently full in Business. Your options are to request a downgrade to economy on the BA service (still a few seats left) or ask for a seat in Business on the ITA service from LHR at 16.55 - but with the flight so far away, it is doubtful CX or BA will do that. Those are the only. flights operating on Christmas Day from LHR, so either drop to Y for the last leg to be sure to get to Rome on the 25th, or travel on the 26th when J class with BA is available.
Pilot37