This Downton Abbey photo contains
boater, leghorn, panama, panama hat, sailor, skimmer, straw hat, fedora, felt hat, homburg, stetson, trilby, porkpie, and porkpie hat.
There might also be
pith hat, pith helmet, sun helmet, topee, topi, dress hat, high hat, opera hat, silk hat, stovepipe, top hat, topper, beaver, and frock.