My first language is not English, as well, and this is one of the reasons why I am always so insecure about my work. One thing that helped me a lot were the english classes. Besides that, I suggest you to just read a lot, write a lot, practice your speaking skills, .... I think that you will get used to writing in english with time. Be persistent and patient!
Is it possible to complete a PhD in the UK when your first language is not english? I would like to think so, as there are many people who have done it before. Probably we need to make that extra effort and eventually we'll get there. But I would love to read about other people's experiences.