Trying hard to remember, but i think the Brits wanted something like that rather than the 5.56 but the US steamrolled them with the tiny cartridge. Might not have been .243, but was bigger than .223.
The British have wanted to go to a .280 even back to the early 20th century. There was never anything wrong with the caliber, it was just world events etc. which kept them from going to it.
I think you are right about them wanting it again in the 1950s but it was the .308 which we forced on them, not the .223.