This movie is so famous that it has coined a phrase: gaslighting. To gaslight someone means to make them doubt their own judgment and personal experience, usually by terming them “myths” or “prejudices”.
People, who have been gaslighted, are generally referred to as “woke”. It’s often employed in show trials, the accused hoping to be redeemed by “confessing” to sexism, racism, white privilege, and so on.
This was a technique much used by the inquisition. Under extreme pressure even perfectly sane people can be led to doubt that the Earth moves, or that there are two sexes, and be ashamed to ever having held such views.
It only works, however, if the victim feels the need to be accepted. In Bergman’s case, it is the expectance of marital bliss, which is only fulfilled, when she accepts her caring husband’s verdict of non compos mentis, each admission bringing her closer to institutionalization.
As opposed to later versions, we never doubt that this is his plan, which is perhaps the movie’s greatest weakness along with Boyer’s manifest villainy as opposed to Bergman’s Oscar performance. The title of course merely suggests the London setting, the fog and dimly lit streets and parlors, so conducive to the pervasive feeling of dread.