OP I don't think some of the advice you are getting here is very good. I am amazed that someone giving advice to an overseas student has not heard of DLD. Or thinks that central London boarding at £14k is excessive.
Lots of overseas, particularly Asian, come to the UK to complete their education, often then applying to UK or other English speaking Universities.
If you are academic I would think about taking your GCSES in a year. This is offered by several London tutorial colleges, certainly Asbourne College (we know a boy who earned 9 A*'s despite switching both system and language) but possibly DLD, MPW and others.
Subscribe to the Good Schools Guide online, look under tutorial colleges and then approach the most promising. They will know more about students coming in from different systems. Do come back here to check you are dealing with someone well established.
Consider colleges in Oxford, Cambridge (there is a college there which is very popular with Koreans though I don't know the name), Cardiff Sixth Form College and Concord in Shropshire. The latter attract a large number of students from Asia and get very good results. Living costs are much lower outside London.
If you can do you GCSES in a year, though 8t is very hard work, you are then in a good position to progress to a two year A Level course.
If you are not as academic you might be better off in a smaller, more English, boarding school. I don't understand American grades but you would need to speak to them individually to see where they place you. They may insist you spend two years taking GCSES. Or one year taking a limited number of GCSES in London and then onto a more typical school for A levels.
It is a big and expensive decision and you might use an educational consultant (the Good Schools Guide might be as good as anyone). But rest assured. There are lots of Asian students making similar transitions. One of DS' best friends arrived from Korea at a slightly younger age but with no English. He has done fine.
(Also there is a very big Korean community in South West London in a place called New Malden. One option might be to find a family you could board with. New Malden to DLD is a straight forward train journey.)