I seem to remember that immersions in the 70s were a little more powerful. Somewhere roundabout 14A. But I may have been mistaken. I must look in my 14th Ed. Regs.
My second house, built in 1968, had an immersion tapped off the ring final with a switched FCU.
Under the 15th, it was permissible to use 1 milli for "power" circuits. In theory, I could have used it to wire some of the shorter immersion heater circuits I have wired, even on a 16A breaker. Indeed at college, we did an exercise proving in certain cases, 1 milli was fine.
Not sure what the rules are now. You could probably use 1.5?
But my go to was 2.5 up to the local 20A DP switch, then 1.5 Butyl to the element.
But I didn't use HR flex.
The comments in this link are interesting, which effectively state that which we probably all agree with, the older accessories were much better built:
Immersion Heater & 13 Amp socket. - Wiring and the Regulations BS 7671 - IET EngX - IET EngX
https://share.google/7i91oTRVGq8JGEHZU