I believe the easiest way to achieve this would be to expose yourself to a lot of British media, and also to make it a habit to exclusively use an English accent when speaking English. You may not get it straight away, but you'll find that with time the accent and pronunciation will begin to feel more natural. As for how long, a month would be enough to see definitive results if you work at conditioning your speech everyday.
I'm Kenyan, so having overcome my own pronunciation issues, I understand your sentiment of wanting to have an accent that is easily identifiable and understood globally. Plus it just sounds nice :)
Ganbatte ne! (^_^)