Korean restaurants in London that I have been to recently:
The newly reopened Busan, in Islington. This was my introduction to Korean food - courtesy of a friend of mine. Service was ok - not particularly attentive but fine, atmosphere was ok (a little cafeteria like), but the food was really good. They have various tasting plates so that you can try different types of kimchi, which was excllent, and we also split their aubergine and sesame starter which was delicious. They had a few vegetarian main course options but I was the only vegetarian in the group so can only comment on the one I had - bimbimbap. Mmmmm, lovely vegetables and little bits of crispy rice and creamy eggness and West Indian hot sauce-like sauce.
The Old Justice - Bermondsey boozer that does authentic Korean food. Yes, really. It is bizarre. It is literally half Bermondsey boozer, half Korean ex-pat hang out. We were the only non-Koreans eating food in there. It's kind of worth going to just to experience the oddness of it. I love London.
Based on another review, which warned that the vegetarian bimbimbap often comes with meat that hasn't been mentioned, I specifically asked about its vegetarian-ness when ordering and was told that that was fine. It then turned up with meat in. The waitress realised immediately and was reasonably cheerful about me sending it back. Based on the length of time that it took to come back and the way it tasted, they definitely remade it rather than just picking the meat out, which is always good! So, er, I would say that you should make extra sure it's vegetarian when you order it but I tried that and it still came with meat. I guess, maybe you could try harder but, probably, it's simplest just to prepare yourself for potentially having to send it back.
The bimbimbap was, when it eventually appeared in its meat-free form, pretty tasty - though I think perhaps not quite as nice as Busan's. The pan fried vegetable dumplings that we ordered as a starter to share didn't arrive until after we'd finished our mains which was a little weird but they were very nice so I didn't find myself minding too much. They have a wide selection of Korean drinks which I wasn't feeling brave enough to try. Maybe next time. It's only a short walk from our house so, even though I think the food was nice rather than extraordinary, I can see us coming back.