There's also Estuary English, which has some features of Cockney, like the glottal stop, but doesn't take such a cavalier view of grammar. Tony Blair, for instance, will often drop the letter 't' when speaking in the UK, though when abroad he tends to speaka more traditional RP.
I presume that what she means is that she is away from Cockney accents- there are wealthy parts of London to the south of Chelsea where accents will tend to be closer to RP. Cockney is more associated with the east and north.
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