That's actually very good. I'd say the accent she's adopting there isn't either the prestige accent that's sometimes called "RP" or "BBC English", or the traditional London "Cockney" accent (which are probably the two accents most heard on media overseas) - but is more like a younger, urban. middle/working class accent - closer to what's sometimes called "Estuary English". You can hear it in the way she says the "a" in "fake", and the way she slurs the "t" at the end of some words. This is influenced by London speech, but is less regional than Cockney, and is spreading to the heavily populated areas outside London, especially among younger people.
I'd say Carrie's picked that up pretty well.
I love it. Carrie can do anything, her Dad is right.