Hi Aspirant,
Yes you can study in South Korea after BA in English. There are several higher study options for meritorious graduates in English language and literature, such as MA in English, journalism and mass communication; management; tourism administration; law; international relations; linguistics; communication management; film editing and direction; visual communication; and library and information science.
Also studying a Masters in South Korea offers a fantastic opportunity to get involved with one of the most vibrant and fast-moving higher education sectors in the modern world. South Korean government support for international students:
1)Around 30% of courses at Korean universities are delivered in English, reflecting the country’s drives towards internationalisation.
2)The Korean government provides financial support to around 2,000 international students each year.
To get into Korean University, you have to satisfy some conditions which may vary depending upon the University. I am listing some of the best universities there, check out the links for more information,
1) Seoul National University

https://www.snu.ac.kr/

2)Sungkyunkwan University

https://www.skku.edu/skku/index.do

3)Yonsei University

https://www.yonsei.ac.kr/en_sc/index.jsp

4)Korea University

http://www.korea.ac.kr/mbshome/mbs/university/index.do

5)Kyung Hee University

https://www.khu.ac.kr/kor/main/index.do

You can check out the foreign students pages of the above mentioned websites for a detailed information on the eligibility criteria and further applications.
Hope this helps.
Good luck!!!