What I found

Recently I moved to London with a working holiday visa. Before coming here, I was really worried about how I was going to get a job, or whether my English was good enough. However, once I was here, I realized that I was worrying for no reason. I was fortunate to get a job, and I can communicate with the English people. Of course, I don't speak perfectly, and I can't understand perfectly everything they say. But I did find out that there are many people in London from different backgrounds, countries and religions, and maybe they were once in the same situation as me. I think that's why they are so tolerant of others. I'll try everything with no hesitation, and I'll enjoy more my  life in London.

Time references, like 'recently', in your first sentence, usually go at the front or at the end of the sentence. Good job with the paragraph; I hope you have a great time in London.