I would concur. Your *A possibilities from LHR to ROM are limited. Don't forget, you're going from a Oneworld shop to a Skyteam shop. Only BA and AZ do direct connections.

Looking at afternoon *A connections, about the only feasible one is on LH via MUC, leaving 15.25, arriving 21.10. The taxes on this route alone come to £52.60, making it a rather expensive award ticket.

With a bit of throwaway ticketing, you could get a direct flight on BA from LGW for £114 (or less, if you're lucky - but it gets heavily booked).

Alternatively, if you want to save money, you could fly on Meridiana, from LGW to Florence, who do a one-way for €86 (including tax). Florence to Rome is about 1h30 on the Eurostar Italia. Easyjet also fly to Naples, about the same distance from Rome, but the timing is less good.