Keep in mind that trains are very reliable, convenient and not too expensive in Europe.
You could even fly in or out of Zuerich, Switzerland and take the train between Italy and Switzerland if you don't find anything better. Zuerich to Milano (downtown) is only around 4 hours on the train and a train every hour. And there is a train station inside the airport in zuerich - which makes it really easy.
If you plan to do more train segments the rail passes are inexpensive.

And i agree: avoid LGW-LHR. It takes forever, is expensive and the London airports are not really pleasant.