Shutters were part of the BS1363 specification from the outset (late 1940s), after which they became the norm on BS546 as well. I'm not sure if there were some shuttered BS546 devices before then, however (there are none of any of the old 1930s sockets I have).
Shutters weren't universal on BS546 adapters. I have several dating from the 1950s, and even early 1960s which have a non-shuttered BS546 5A socket on the front.
Of course, none of the two-pin, non-grounding sockets ever had shutters.
non-grounded sockets just don't exsist at all in the UK
It's probably fair to say that that's the case in 99.9% of homes these days, but old two-pin sockets survived for a remarkably long time.
There were certainly still a large number around in older houses when I was a kid in the 1970s, and even as late as the 1980s I remember seeing some (typically where new rings and BS1363 outlets had been installed but the house still had its original lighting circuits, including 5A sockets).