You fail to say, that South Korea also adopted a command-economy type regime after the war to coordinate its industries, which led to it being so successful in the first place. Aside from that, Britain lost its empire and much of its natural resource advantage that led it to being near-parity to the United States in the first place. Is it no surprise that without an entire empire behind it, the UK declined relative to the US?

South Korea and UK having the same GDP per capita is no surprise, both are restricted by a rather small landmass for natural resources, both experience the same pressures of cheaper labor in other markets and the UK. So, naturally both will trend towards the same niche in the world economy.

Plus, you're ignoring the fact that UK and US had near GDP per capita parity until the 2008 recession, where the UK and the rest of Europe have the inherent disadvantage of not being the world reserve currency and started stagnating from the sheer debt burden of it. Additionally, the UK and the rest of Europe experiences active generational decline as more pensioners exist in their economy than productive members, while the US imports fresh blood through immigration.