First place that jumps to mind is Richmond! Radio 4 is certainly more "chatty" while still being posh and Richmond is both posh and full of that street/café life.

If we're going to fill out the roster, let's say Radio 1 is Camden, 1xtra is Brixton, Radio 2 is Bromley, Radio 5 is Dagenham, and 6music is eh.. I dunno, Shoreditch?

Radio 4 has to be Westminster, surely? And Bloomsbury in the evenings.

Richmond teeters over into Classic FM to my taste - ostensibly cultured, but basically posh-pop.

And LBC is a diffuse torroidal agglomeration of zone 3+ greasy spoons known only to White Van Men and black cab drivers.

Maybe! I am not really an R4 listener and when I am, it's for the twee comedy stuff rather than the news and politics. If LBC is as you describe, though, I dread to imagine where Talk Radio is :-D