One thing I have noticed about impersonating accents is that they often drift through regional dialects. Someone doing a "British" accent might start Queen's English, slide into Educated London, drift into Cockney, and meander through Yorkshire to Scottish, aye?
It might help to have a specific person whose accent you are mimicking in mind - maybe even a picture of them in front of you - to keep you on track.
Oh, stuff it, just drop a lot of "I say" and "Don't you know" and "old chap" into the text.
