I cycle in London, UK all year round, and share many of your opinions/discoveries. Although I don't wear wellies to cycle in; I either use my SPDs (which get wet unless I remember the overshoes), or ride in DMs.

I did also when I still worked in an office keep a spare pair of knickers in my desk drawer, and either kept Emergency Change of Clothes there or cycled in bike kit & had office kit in my bag. This mostly after an autumn morning when I got so wet on the way to my (unheated) office that I had to go down to the High St & buy myself a new skirt to avoid getting pneumonia.