Did British Empire and South Korea exist in the same era?

Yes, the two civilizations both existed around 1948 CE.

Which lasted longer, British Empire or South Korea?

British Empire lasted longer (414 years).

British Empire: Avrupa; South Korea: Asya

British Empire (1583 CE – 1997 CE) and South Korea (1948 CE – present) lived in the same era.

The empire with the most extensive territory in history. It was referred to as "the empire on which the sun never sets."

Republic of Korea · Asia

Did British Empire and South Korea exist in the same era?: Yes, the two civilizations both existed around 1948 CE.
Which lasted longer, British Empire or South Korea?: British Empire lasted longer (414 years).
Which regions did British Empire and South Korea rule?: British Empire: Avrupa; South Korea: Asya