Brighten up your lino by painting it with “Darkaline” stain.
Judging by a number of posts about attempting to remove 1930s “Darkaline” stain from wooden beams and the like, on DIY talk boards, it seems it did indeed provide a very lasting, highly-polished finish. It possibly contained shellac to give the hard-wearing shininess.
For other shiny floor options, why not just spray some wax on your floor?
The modern equivalent for me is attempting to cover shoes with “protector spray” from the shoe shop, which provides a helpfully lethal, friction-free surface coating for the floor.
Anyway – no wonder a public information film had to be circulated about the dangers of the “fatal floor”. “Polish a floor? You may as well set a man trap.”
https://m.youtube.com/watch?v=vt016gTNp_k