I've been in London this year to study English and the city is amazing. You should think about climate because for me as a brazilian, it was really hard... everything is grey and sometimes I was depressed. I adviced you to go there on March because on this month the spring starts and everything changes, the mood of people, the landscape, there is a lot of concerts, events.
You should be careful because in London there is a lot of people from all of countries in the world. Yes, this is good, this is amazing but be sure that there is a lot of people from your country too and you should go away from them. If you want to improve your English you should avoid it. It's hard because if you feel alone you'll definitely looking for friends from your country.
I was really happy and I'm sure that I choose the right place to go. British people speaks English really well and correct. In London there is a lot of museums that you can go for free and a lot of activities. I've been missing it a lot.