Alan,
I agree with Frank but would say this Itinerary is very exhausting! Whether it's "doable" is a matter of opinion, and I suspect it's going to be very difficult to keep to this schedule given the distances you're travelling and the "variables" that could occur. Anything to add - I don't think so!!!
I'm sure you've heard the saying "the best-laid plans of mice and men often go awry". This schedule will be possible ONLY if everything goes as you've planned. One thing I've found in traveling in Europe is that "unexpected events" often occur without warning (a "manifesto" in Italy for example). If that happens, it will throw your carefully planned schedule for a loop!
A bit of clarification on London - I'm assuming you mean the "Tower Bridge" (isn't the London Bridge at Lake Havasu?). Regarding the Changing of the Guard, as I recall at certain times of the year this only takes place on even or odd days (July/Aug. this may be every day, but I'd have to check).
In Paris you indicated "Find home base". Does that mean you won't pre-book lodgings? July/Aug. is PEAK travel season so everything will be crowded, and that's another reason why this schedule may be difficult to achieve. This is not the best time of the year for spontaneous travel in Europe!
Visits to the Museums in Florence will also require reservations (unless you don't mind a hot and crowded queue which could take many hours).
Some of your rail trips will require reservations, and you didn't indicate if you were planning to travel with a Railpass or P-P tickets?
Although I'm reasonably familiar with getting around Europe efficiently, I wouldn't even attempt a trip like this.
Good luck!