Also watching TV or listening to the radio very attentively can help you to hear native pronunciation and rhythm. Don't be afraid to mimic the sounds and don't worry if you think you sound silly. The more you practice the better you will become.

All good advice, but do remember that there are many, many English native accents. "proper" is a difficult term to define for English pronunciation. I met some Japanese students who spoke good English with a Scotish accent. They wonderfully adopted their teacher's accent.

The best way is to practice with native speakers. If you can find a native speaker who wants to learn Tamil, then you might be able to do it for free as a language exchange. But if you can afford the cost of professional lessons, find teachers on iTalki and talk with them regularly so that they can help you with your pronunciation.