There are some basic pronunciation that you must learn to be understandable but don't worry too much about removing all traces of your accent. Afterall, the accent of an English speaker from England is different from that of the USA or Australia or Canada or South Africa. We all have slightly different accents but we can communicate with each other.
From a personal point of view, I find several foreign accents to be quite pleasant to listen to when they speak English.
Your object should be to speak clearly with the correct stress on the syllables of a word and the correct stress on the words of a sentence.
Whether you have a perfect British/American or other accent is not important.