As an Englishman (wow, writing that made me feel very 19th century for some reason) I would like to say that I am a big fan of the accents - keep 'em coming.
One thing that does annoy me (just a little) is the conflation of "English" and "British". Your "British accents" are always English. At one point you even talked about British as opposed to Scottish accents, whereas, as I'm sure you know, Scotland is part of Britain. I know a lot of Scots probably don't want consider themselves "British", but that doesn't mean it should be used as a synonym for "English". You'd never hear anyone over here refer to a "British accent" - there just isn't any such thing. Of course, accents vary widely within England itself too, but talk of British accents just sounds weird...
Not hugely important, I know, but it does wind me up
ever so slightly. 
But like I said - the accents are great, Jay. Don't let this put you off letting rip with a few "cor blimey guvnor"s when you feel the urge.
I also agree that Randi speaks was poor. And as much respect as I have for the man, and as likeable a character as he seems to be, I don't generally look forward to his segments.