You Do Need power plug adapter while traveling from United Kingdom (UK) to South Korea.

Here is Why You Need An Adapter

The outlet and plug type used in South Korea is F and in United Kingdom (UK) is G. This is how they look like.

United Kingdom (UK)

In United Kingdom (UK), outlets of type G are in use.

Type G

South Korea

In South Korea, outlets of type F are in use.

Type F