Tiaras have never been anything but an elite fashion. They're mini-crowns - often part of a full set of jewelry. And the modern fascinator is very modern, probably dating to the 1990s at the earliest, so there's not much to say about them here.

Hats and veils, however, have a long history as everyday dress for women at all levels of society. I have an answer here about the decline of hats (mens, but the story is roughly the same for women's) in the twentieth century, and I discussed changes in women's headwear over a longer timescale in this other answer. As they became too formal for normal everyday dress, they became more associated with people who dress formally more frequently - the upper classes.