I'm not entirely sure what the process involves (as a speech therapist, I'm not very positive about it!), but perhaps there may be an elocutionist that you can receive elocution lessons from. I could recommend some books - Alan Cruttenden's Gimson's Pronunciation of English is good if you have a sound phonetic background, and it focuses on RP. It would be very hard to learn an accent just from reading books, however, so listen to as much English as you can trying to keep to the accent you want to learn.
If you want to learn RP, this might be harder to do using BBC television or radio. The current trend in Britain is for television and radio to use regional accents. The days of the news being read in an RP accent are largely gone. There still exist some RP accents around in the media though - any Royal Family member, Stephen Fry, Rowan Atkinson (Mr. Bean) are a few who come to mind.
Without a doubt, however, elocution lessons would be the best thing to do to master a particular accent.
I would also recommend recording yourself and listening to it objectively, and ask yourself if it sounds like the target accent.
Student or Learner