I guess every actor will handle this differently but it's something I've had to do (because I come across as a bit of posh bird apparently

). I find it very hard to tone down my RP without sounding bored or false, so I would probably elect to do another accent I am comfortable with and opt for the posh/well-educated end of it. So, rather than dropping any consonants in RP, I might choose an accent where consonants are often dropped but aim for reasonable diction within the accent (because that sort of suits the kind of character I would normally be cast as). Does that make any sense? I find it quite hard to change my own natural RP, unless it is to "heightened" RP - which might be handy for Noel Coward, but isn't much help for many other castings
