How much aid does UK give to Korea?

There is no such country as "Korea".

There are North Korea and South Korea.

North Korea -

Recently due to the flooding in North Korea (in 2012), the UK sent emergency food and medical supplies to those caught in the flooding.

North Korea is actually hostile to the UK and is one of the UK's most dangerous enemies. The UK would have preferred to not aid North Korea at all, but it has not choice because, as a member of NATO, the UK pledges to support disaster victims globally.

South Korea -

South Korea are one of the UK's closest allies. The UK aids the South Koreans by trading weapons, ammunition and military vehicles to so South Korea can defend themselves against the hostile North Korea.

South Korea and the UK also exchange intelligence on North Korea for the security of both their countries.