[zerocrates]

The usual touchstone case in this area in the US is Bridgeman v. Corel, which came down on the side of "no copyright" for these kinds of reproductions:

https://en.wikipedia.org/wiki/Bridgeman_Art_Library_v._Corel....

That's an appeals-court level decision so there's some wiggle room to claim that the rule on reproductions isn't totally settled. UK law is a little different and, to my knowledge, somewhat less hostile than US law to a "sweat of the brow" argument about the labor and skill required to produce something possibly bringing about copyright protection. Still, my understanding is that the current situation in the UK is much the same as in the US.

Regardless, it's still fairly common for museums and archives in the US and UK to assert copyright in scans and reproductions they produce, even if they generally don't ultimately follow through in court. There was a high-profile dust-up between the National Portrait Gallery of London and a user who was uploading high-resolution images to Wikimedia Commons, which resulted in much saber-rattling but no actual case.

Simply making the content unavailable and requiring agreement to a contract or set of terms seems to be the main method currently in use for these institutions to try to maintain their revenue streams from reproductions.

[zozbot234]

My guess is that the "revenue streams" from reproductions of public domain content are (1) negligible to begin with, and (2) might even be higher for many institutions under a permissive policy, since paying for the institution's implied endorsement would still be a highly-sought-after signal for most serious commercial reusers. Many institutions are starting to realize this, even in Europe where these overblown copyright claims used to be even more common.

[tingletech]

I think this is true mostly, but not all cultural heritage institutions are on the same page here. I work on some sites that serve the cultural heritage community, and last time I talked to some of our larger contributors, reproduction rights were still a revenue stream that was large enough to want to maintain. For some contributors, it is not worth their time to try and deal with licensing.