Watch English-language television and movies originating from Great Britain. Whether this is in the form of newscasts from the BBC or popular reality TV shows and sitcoms like "The X-Factor" or "Skins," exposing yourself to authentic language spoken by native speakers of British English will expose you to a wide range of vocabulary -- both colloquial and, in the case of newscasts, formal -- you might not see elsewhere.
Read British magazines and books, which will further help to augment your vocabulary. Doing this in concert with television and movies will expose you to spellings and sentence structures, details you might not be able to glean while listening or watching video media.
Build relationships with any colleagues or fellow students who originate from the United Kingdom. By engaging in English-language conversations with native speakers of British English, you will increase the likelihood of picking up their nuances and expressions, rather than American or Australian ones.
Make an appointment with your academic advisor or a human resources representative at your company to investigate transferring to the United Kingdom, be it for educational or employment purposes. Although befriending British natives and partaking in written and visual media from the isles will help you gradually acquire the language, there is no substitute for full immersion.