Based on the OP's situation and price quotes, BA F would be my recommendation.

LH F is excellent when it's good (and the 748 is wonderful), but the service and wine list can be variable. BA F is functional, with earnest attempts at good meals, and great alcohol onboard and in the lounges (especially at your LHR connection to Italy). UA C actually has a VERY good wine list these days; unfortunately, the food is no good.