Whenever I stay at my Japanese house, I work as an ESL teacher for a conversation school over there. This has brought me into contact with many people who hope to increase their English language skills for university studies, for business, or just for fun. One of the best ways to do this is by studying abroad in an Enlgish-speaking country for six months, a year, or even longer.
If you want to improve your English while living in London, check out Answer English – English for Fun. The English for Fun courses allow students to learn English along with doing something fun, such as playing tennis, going horseback riding, studying fashion, and more. I know from personal experience that students are much more receptive when the learning environment is enjoyable, so this sounds like a very interesting school. Check it out!