Firstly I would really like to acknowledge you and commend you on your desire to improve your English communication skills. I always think that wherever we travel to settle in the world, it is so important to take the time to deepen language and cultural knowledge of the place which is our new home and to get to know the customs and the people.
Regarding deepening English communication skills, I would really recommend reading as much as you can: newspapers, magazines, reference books on all topics and novels. If it is really a question of achieving a better language level, then I would suggest setting yourself daily grammar goals, starting right from the basics and building up day by day.
If you can, try and invest in a good English grammar exercise book, with pages and pages of exercises for English communication skills that you can auto-correct with the answers at the back. For example, the Oxford Practice Grammar series – start off with the elementary level and then work yourself up. Alternatively, online, you can find endless grammar exercises for free nowadays. So I would make yourself an index of the crucial grammar points and then work through them. This will strengthen the basis of your language and give more confidence in the construction of sentences.
For spoken practice of your English communication skills, I recommend speaking as much as you can with as many people as you can. At first, start with normal daily interactions like shopping, dining out, etc. Then try and expand your social network in any way you can to widen topics and vocabulary. If you have some native speakers around you and you have a good friendship with them, ask them to correct you as much as possible so that you have continual correction of any mistakes you may be making.
And as much as I resist telling people to watch TV, here TV is a really excellent language learning tool. Listening and understanding are enhanced by watching TV or listening to the radio and you have a wide variety of things you can watch or listen to. Try watching TV with a notebook at your side and jot down any words that you have not recognised so you can later look them up to get their meaning.
If you are working in a company then try and observe meeting behavior and language. Again check out on the Internet “English language for meetings” or “English for negotiations.” Always look up the language or type of language that you are interested to improve.
It really will not take you long to get to a much deeper level of English communication, especially if you are working step by step to improve it on a daily basis.