Vegetarian Options

Google vegetarian eateries in all of the named cities (and especially London - try any Indian place where the food is, by the by, fantastic). That said you'll have no difficulties ordering a vegetarian meal anywhere in Europe. Since you say milk products are fine anything with say cheese will give you plenty of protein, and yes fat and calories. My eldest son's best friend is a strict vegetarian (religious reasons going back generations) and they had no problem when traveling together a few summers ago. This is not to say that you can always get a balanced, yes balanced, vegetarian meal (my son's friend doesn't eat dairy for example) but this isn't a life long diet you're considering.

You will have no trouble finding vegeterian food in Switzerland,Italy or London. My wife and I are both vegeterians and have no problems in most of europe.

There's even vegetarian doner kebap, super yummy.

My wife is a vegetarian and has rarely had any problems ordering and we eat most of the time in everyday restaurants as opposed to specifically vegetarian. I do think that if you were a strict Vegan you would have some difficulty, if only in language barrier, inquiring as to the contents of a dish. It is easy to communicate "no meat", harder to determine if they are sauteing those vegetables in butter or other minor prep techniques.

I just noticed you say that you don't eat eggs, although milk and cheese and (presumably) butter are okay. The "no eggs" thing will make it a touch more difficult, since eggs go in mayo, some cream-based sauces, and many baked goods, as well as being used in breading and other food prep. I've been in Europe when I was vegan, and ended up eating rather a lot of grilled veggies and salad, oil and vinegar on the side, to be on the safe side. If you check menus via the web, and then err on the side of Indian food, Thai food, Chinese food, etc., you should be fine. But I would DEFINITELY learn how to say - or print on a card you can flash - a phrase like "We do not eat eggs, but can eat meat and cheese and milk. What can you recommend on your menu?" in the local language. And then... you will have to trust the wait staff. I know from talking to friends in the industry that, well, sometimes they are not precisely accurate in their response to your special order if they think you are just voicing a preference, not an allergy or medical condition. Sad but true.

Kira - The way to fix that problem is to add to the bottom of the card in the local language. "Fatally allergic to eggs" Granted it would be a lie and some folks are unwilling to do that. But if you are worried that some well meaning but misguided wait staff is going to expand your food choices because they don't agree with vegetarianism/veganism I doubt those same folks would do so if they thought it would kill you. Most folks who are unwilling to accommodate others food choices that are based on ethical consideration, religious choice, or simply taste choice (e.g. my sister's dislike of peas) are typically willing to make such accommodations if they think it is an allergy.

I go along with Ed on this one. People may not think about trace amounts otherwise or simply not take the "no egg" too seriously.

Try www.happycow.net, someone on the "to the north" site sent me this site to check for vegetarian restaurants/cafes in Ireland. They list by city, so if I knew we were going to stay in that city I made note of the veg. restaurants. They also list health food stores by city. I am not sure about the no eggs, but I did not have any problems finding food to eat in Ireland. I did eat pasta, which I believe eggs are used in making noodles. (I noticed you would be in Italy.) We used RS book for recommendations and would also ask our B&B hosts for suggestions. Nearly every restaurant had a vegetarian option. Several times the chef would come to our table to ask what I would prefer offering me several options. I found restaurants willing to accomodate. Some of the best food we ate was prepared at vegetarian restaurants. When we were in London, a few years ago, I found many vegetarian friendly restaurants there also.
Barbara

Being vegetarian and also vegan is extremely popular in many countries in Europe, so restaurants are catering to their public. I spent quite a few years being vegetarian, and often just asked the kitchen to make me a veggie plate, with maybe some potatoes or rice extra. Used to get these beautiful platters sent out that made all the meat eaters at my table jealous. Fresh, local produce is popular and you will find this on menus, as featured dishes. When it is asparagus season, or strawberry season, you will know. Right now, all kinds of mushrooms are flooding the market stands, as well as huge nectarines, peaches, black-berries, and apricots. All the cabbage family veggies are on their way too, brocolli, cauliflower, brussel sprouts, and the squashes, like zuchini and pumpkin are arriving too. So, Guten Apetit!

I heard of a restaurant in Texas where the vegetarian option is chicken!