In order to keep more than one pass through the Xray in ASA 100 and 200 films, I get "same day process" and print. You can't do it with chrome or with medium format so I always 35mm. Europe is loaded with Kodak films, I often had to search around for Fuji Superia.
I was in England last July and in France this May. Both times had about 15-20 rolls of ISO 200, 400, & 800 35mm as well as a number of Sony memory sticks. All with through the Xray about 3 times and I had no problems. The ISO 800 was used in the British Museum and in the Louvre and the prints are great. Outdoor shots with ISO 200 are very sharp with no unexpected grain (except when I had my FM3A set wrong . . .)
As was said anytime is a good time. Don't be afraid to take some high speed 400 and 800 for inside shots with or without flash depending if it is allowed. Just make sure you put the film in your carry on luggage. A lens goint to 200mm is nice to have from time to time for isolation of some scenes and a 28mm to get some of the buildings. If you get into any castles, try to get up to the turrets or other high spots, you may have to get to the towers by going through a pay area such as a museum or the like. Carry enough change for unexpected moments.
You will probably find that a polarizer is needed, especially around Lake Como and other areas where there are mountains in the background. I always have had a grand time. Think about how much film you want to take, then double or triple it. It is not that it is hard to get film it is the 9 to 12 Euro that kills it. Enjoy -- Bon voyage.
When I last went to London, England I was not aloud to take pictures inside historic places like the tower or london ,buckingham palice, windser castle and so on. One reason I can think of is because they want you to buy the year book guide to each place so they can get more money. Plus also I think for security reasons.
Part of the problem with shooting in historical palces like this, Chris, is that repeated flash exposure has a deleterious effect on many things, including historical documents and other items. Not everyone uses flash in situations, but instead of having to justify why someone with an expensive camera and proper film should be able to shoot, while the guy with the P&S and flash is not allowed, is more of a headache than many places would care to endure. Thus they decide to prohibit photography altogether. Of course, they still would prefer they buy the souvenirs they sell, but it also has to do with preserving what they have so that future generations will be able to appreciate it, too.
As Jeff indicated, those who know about photography have to pay for those who know nothing. I was in Versailles a few years ago, and a German national who had a P&S decided to ignore the large signs of "No Photography". He even shrugged his shoulders when I pointed them out to him the minute I saw him take the camera to his face. You should have seen his attitude when the guard ran to him and gave him a very French lecture on the nature of public signs!
Oh, by the way, I try to solve the fast film dilemma by carrying only ISO 100 and 400 slide film rolls. If I want to use my zoom or shoot in low light, I take a 400 roll and push it 1 stop.
Good luck, photodrew, but remember: always ask before photographing. Sometimes in the heat of the moment we just don't notice the signs!