How can I become fluent in English with a British accent?

That is not a matter of concern in the slightest. Spend your time and energy into focusing on correct pronunciation, something which can absolutely be accomplished using your very own regional accent. Accent is simply put the geo-lingual product and result of where you first spoke. It has no relevance whatsoever to fluency due to proununciation being affected by the surrounding speakers who have influenced your tongue. Accents, and dialects for that matter, are worthy topics in sociolinguistics and not perfection of language.

I do assure you that it is a matter of practice. The more you practice , the more you learn.

Only via direct communication with Brits, chat with them and travel to UK or Australia