I come from S London too but I have been told that I have an unplaceable accent. I think that over 30 years of working internationally (although 25 of them sitting in London) has eroded my roots!
'BBC English' is a nice way of describing accentless English pronunciation with perfect grammar.
But that doesn't cover the shrill whining and braying that you do hear from some of the lads and lasses that graduate from the top Universities of the UK.