I work in a rural school in East Anglia, populated by quite middle class, predominantly right wing and privileged students. When they're with their mates, they say "oh my days" in the same way as they say "bruv" and "innit". I remind them regularly that if they ever go to Actual London and try speaking like that, they'll sound like complete wazzocks.
It isn't twee at all. It's London slang and said, ime, in a very particular way.