You can use the price comparison site to find the cheapest available flights to Korea. Often you get better deal if you plan ahead and are flexible with the travel time.
Here is the list of the sites for you to get started:
www.skyscanner.net/flights-to/kr/cheap-flights-to-korea-(south).html
www.cheapflights.co.uk/Korea/
www.lastminute.com/site/find/World/Asia/South-Korea/South-Ko
www.tripadvisor.co.uk/Flights-g294196-South_Korea-Cheap_Disc
www.ebookers.com/
It is important to check the site that you are going to purchase tickets from has a ATOL (Air Travel Organisers' Licensing) logo and a secured payment logo (listed as below).