air flight

What you want is a "multi city" itinerary (also called open jaws). Don't look for one way tickets across the Atlantic, as those are MUCH more expensive. To find these, go to www.kayak.com. Choose "multi-city" rather than "one way" or "round trip." Put in your first segment as Louisville to Naples (make sure it's NAP, not Naples, FL), then put in LON to Louisville as your second segment. For flights from Naples to London, use www.skyscanner.com. This will pull up bduget carriers as well as others. Be aware that there will be extra charges, but you can still get a good deal. Also be aware that London has 6 airports; some are quite far, and it will take time and/or money and/or hassle to get from them to London (Heathrow, Gatwick, and London City are closest and easiest). Even if it were "cheaper" to fly round trip to London from Louisville, you have to figure in the time and money you waste backtracking, as well as the risk of missing your flight and having to buy a new one if they are booked on separate tickets. You should also try a 3 leg multi city trip on Kayak: Louiville to NAP, NAP to LON, and LON to Louisville, just to see if this works better than buying the NAP to LON separately.

Beside what Harold mentioned, also try the following: SDF-LHR Round trip. This will put you in London. Delta, United, USAir, American (or British Airways), can get you to London Heathrow from SDF through their respective hubs back East. Then from London you could buy a round trip ticket on a low cost airline. EasyJet flies to NAP from both London Gatwick (LGW) and Stansted. LGW is closer. There are also seasonal charter flights from Gatwick to NAP with Thomas Cook and Thompson. If you split the flight this way make sure that you have enough time in London in both directions. Even a full day. That way you have enough time to transfer airports, since your flight from the US is likely to land/take off at London Heathrow, which is not used by low cost carriers. Since you want to spend a week in London. Maybe you may want to spend six days in London on the first leg, on the way to Naples, and then fly back to London from Naples for another day in London, the day before your flight back to the US from London. Unfortunately there are no flights to/from Naples from Heathrow, therefore you need to change airports in London no matter what. Having 24 hours to do so helps.

The Louisville Airport is well serviced by U.S. Airways, and their gateway city to Europe is usually thru Philadelphia. Your alternate way might be Louisville-Philadelphia-Rome FCO. Then take the 20 minute train into the city and a 2 hour fast train to Naples. On the return, you could catch a budget air carrier EasyJet.com from Naples to London Gatwick. Then go London Heathrow to Louisville on U.S. Airways. You'd just have to price out the Multi City flights on one of the big travel websites and figure out which is the cheapest. Often he cheapest is not actually the fastest or most inexpensive way--if you have to layover a day.