I would have fingered Dream Academy as absolutely archetypal except I can't seem to find much evidence of them wearing hats
They do have headgear of varying kinds on the cover of this though
The wide-brim hat seems to go hand in hand with a non-rocking, wussy innocuousness, combined with an over-layered, slightly florid thing
It's these fine fellows I think who are the actual archetype - and again I'm not sure if it's even "wide brim", it's just hat-wearing - that was a real thing on the indiepop scene 1984-85-86
Ha! Look! I was right - in this TV clip from the show Wired, the presenter who's introducing Martin Stephenson and the Daintees is wearing one of those hats, and he stops right in front of a hat shop, and he says "they'll be banning hats next" (in reference to some Thatcher government measure against homosexuality).
Who else had hats?
Who - at least for the duration of the first four singles - are not Bad Music Era at all - in fact I really liked them.
Interviewed them around the (disappointingly wussily-produced) debut album Giant, which did have a few lovely dreamy tunes like this one -
- but overall got a bit sickly and spoiled by overproduction.
You can forgive any hat-wearing tendencies when it's muscular driving trancebop like "Well Well Well", "Move Me", "It Will Come" - but when it gets all wispy and wimpy, the hats start to seem like the problem...
Who else then?
I might have fingered Microdisney as culprits, but on quick glance can't see much hat-wearing evidence and I'm not going to start poring through old videos, that's for certain (never cared for their supposedly subversive-MOR sound)
James (like the 'Tops another group I liked then - but only for a moment) appear to have gone bare-headed
Aha - Virginia Astley had a big old hat in the photo sessions around her second album, 1986's Hope In A Darkened Heart, as you can just about see from this cover.
I am not sure that a woman wearing a hat of this kind is so potentially culpable as it is when a man does it, though. However it does go hand in hand with some wispy, florid, non-rock-instrumentation-bedecked music, though, in Ms Astley's case. The strawberries-and-cream dove-toned Englishness of her music would have been something I'd not have been able to stomach at the time - but nowadays, an aging expatriate pining for the rolling hills and horse chestnut trees of the motherland, I have developed a fondness for it. Perhaps it can even be considered part of the proto-canon for hauntology.
The Blue Nile put out an album actually called Hats, of course - with a chap on the front cover wearing a hat - but I don't think they took to going hat-clad onstage or in photo sessions. The Nile didn't really have a look as such - nor would I be able pick any of them out of a police line-up.
Lots of good suggestions coming through in the comments, e.g. Fairground Attraction
Andrew Parker sent through some thoughts:
And yeah with the Mission / Nephs and with G'N'R, it's definitely something else than the Daintees / Woodentops idea
Perhaps what is needed is a typology of Eighties alternative music millinery! c.f. the leather cap look mentioned in the comments.
Bit more from Andrew
I was going to mention the Waterboys and then forgot, although their sound is a bit more epic and windswept (the Big Music - cf. the hatted tendency of U2 circa Joshua Tree)