BA certainly do a few routes, to Heathrow and Gatwick (which aren't ideal for us, but should be good for you)
Ryanair do lots, mainly to Stansted (which is not too convenient or you, but convenient for us). It pains me to say this but Ryanair have improved a little in recent years. Gone is the irritating landing advert, and they aren't as aggressive with customers as they were. They even stopped checking cabin bag sizes, though as so many were abusing this leeway, I'm actually supportive of them picking out the worst excesses and forcing them to pay to put bags in the hold. As for hold luggage, at least at the Italian side, they are now much more relaxed about hold luggage weights. I'd expected to have to shuffle some weight between hold and carry on, but they waved it through with a smile.
Easyjet are similar to Ryanair, but never quite as nasty. They mostly base out of Luton, which isn't great for us, and not really ideal for you.
Definitely worth checking local airport sites to see what flights go there. I checked Southampton and they are showing a twice weekly flight Verona - Southampton in summer.
http://www.southamptonairport.com/destinations/italy/verona/
Southampton is very convenient for Dorset, just one county across
Bournemouth, even more convenient and it shows Torino, Napoli and Verona.
http://www.bournemouthairport.com/destinations-and-guides/a-z-list-of-destinations/
Even if this costs a bit more, there is less pain flying into a smaller provincial airport, than the likes of Gatwick, Heathrow, Stansted, Manchester which are all very busy / hectic.
