Please, please, please tell us where you're flying FROM, as well as TO, when posting question like this. It would have saved me a lot of typing!
However the ONLY place to look is the websites of the relevant airlines. (Skyscanner is good, but imperfect). So here goes:
The following airlines serve Rome Leonardo da Vinci (Fiumicino Airport) from the mainland UK:
Alitalia (from Heathrow)
BmiBaby (from Birmingham)
BA (from Gatwick & Heathrow)
easyJet (from Bristol & Gatwick)
Jet2 (from Glasgow, Leeds/Bradford, Manchester & Newcastle)
Monarch (from Birmingham, Luton & Manchester)
Rome Giovan Battista Pastine (Ciampino) Airport is only served by Ryanair. (Unusually, Ryanair's flights actually land closer to the city centre than those of other airlines!). They operate from East Midlands, Edinburgh, Prestwick, Liverpool, Gatwick, Stansted & Manchester.
Ryanair is currently showing prices (from Stansted) of around £230 return in October (total for 2 adults, including taxes and charges but excluding baggage and card fees)
bmiBaby is offering around £160 for 2 people (total, as above) ex Birmingham, midweek in October.
Monarch's total figure (ex Luton) for the same dates is around £254.
easyJet (ex Gatwick) only want a total of around £142.
Jet2 (ex Manchester) are quoting a total of around £197.
BA, ex Gatwick, comes in at around £230.
Alitalia can be Booked for around £210 in total (from Heathrow).
After typing out all of that lot, you'll probably tell me that you're actually flying from Belfast or Dublin! Oh well, I did my best ;-)
Chris