I don't think that's correct, most plumbing + municipal sewage in London was built in the mid 1800s, whereas hat-wearing persisted well into the mid 1900s.
Hat-wearing might have become fashion. Not that much different from a watch having become fashion, while the functionality of a watch and added value is not that much as it used to be.
I don't wear a watch anymore because I am already required to carry a phone and the phone has every possible function the watch would have. What is the value in the watch at that point? Since I do not check the time that often (there are three clocks on computer desktops/menubars plus a wall clocks in eyesight of me right now) there is little value in having the added convenience of the wrist over the pocket for checking time.