My brake cable snapped while riding my (80s road) bike one day so I replaced it.
After replacing I noticed that the piece fixing the housing to the brake was missing so that when I pulled the brake lever the housing comes too and it doesn't move the brake.
My questions: what is this piece called, and is it something I can buy separately, Is it something that comes with brake line housings, or is it part of the brake lever itself?
They're essentially part of the brake lever. They don't really have an agreed-upon name. Probably the closest is "mushroom ferrule," which appears to be what Dia-Compe calls them.
They're not totally universally sized. Different brake levers have slightly different bits that go there but do the same thing. That said, the ones on the great majority of bikes with applicable levers are all the same size, which I believe is basically Dia-Compe and clones.
You can just buy the common size ones new. In the US, J&B Importers (one of the largest parts wholesalers) has a house brand one they call a "Cable End Button" and UBS has one they call "UNIV BRAKE CABLE ADAPTER." There's also Dia-Compe part 94, same thing. You can just order any of them from an online reseller, or find a shop that has them. Some shops will also have old levers around to cannibalize.
If you mean these things, they’re called cable ferrules — or more specifically, brake (cable) ferrules. Some people also call them cable ends or cable caps.
They’re cheap. Your local bike shop can give you a handful for a euro-dollar (or for free depending on how much you patronize them).
Looks like the component in question is part of the levers and might be a barrel adjuster. BTW that style of lever units with the secondary levers accessible from the tops are known as 'suicide levers' around here.
I would call them cable ferrules, but that same name also applies to the round cylindrical brake and gear cables like
Your best bet might be to troll through ebay, or to search out classic bike parts resellers or breakers.
If you don't care about period look, then a set of more modern brifters could work for the brakes alone, and keep using your existing separate shifters.
These ones are part of the brake lever, and are generally hard to find separate. Plus there's a lot of variation in diameters across brands.
These are intended to take the strain off the very end of the cable housing, and reduce the likelihood for the cable outer to bent sharply as it exits the top of the lever. So they don't sit quite flat in the top of the brake housing.
Your last resort might be to mill something up from a block of aluminium. I've made a gear cable endstop and while it was many hours of fiddling, the result worked well for me. Assumes a level of mechanical competence and access to a lathe and drill press, and inordinate amounts of time and dedication :)
