I can't go back to the 30s but certainly in the 50s those UK sockets that were 3 pin (certainly 5 amp and 2 amp - not sure about 15 amp size) could also take a 2 pin plug for non earthed loads.
No they couldn't. Or rather not officially. The pin spacing between two and three round pin sockets was different. There were some plugs on the market which would fit both though. IIRC Clix.
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