Again, this is all just stories I've heard.
And those stories are quite correct.
BS546 was certainly used with DC supplies in the past, both the 2- and 3-pin versions.
As you say, when a 2-pin plug was used on a live-chassis AC/DC radio or TV, the user had to reverse the plug in the outlet if it didn't work on the first attempt (the tube filaments and dial lamps would glow, but with incorrect polarity there would be no HT/B+ voltage).
If you had a 3-pin plug, you'd have to undo the connections and reverse them.
Yep -- Which meant that if you had a radio with color-coded cord and lived in a house fed from the negative "outer" pole of the supply, you'd need to deliberately connect red to N and black to L in the plug, the opposite of normal.
The BS1363 plugs, at least the older versions, carried "AC ONLY" warnings on them.
I don't recall seeing BS1363 plugs so marked, but some sockets certainly were. I always thought it was primarily where the switch wasn't a quick-break type and thus unsuitable for DC.
So far as I'm aware there was nothing in the original BS1363 specification which limited their application to AC. When BS1363 was introduced in the late 1940s, a good many older urban areas still had DC supplies.