Thinking about it, Ttbb - you're probably right.
I'm a Kiwi, and we're also taught the RP away of saying words - it just comes out sounding different, because our accent comes in to play.
Kids are 'taught out' of saying things like 'f' instead of 'th' (and it certainly takes some children longer - by adulthood though, no-one except someone with a speech impediment would pronounce it 'f'), etc. There are no glottal stops, or 'we was', 'I seen', etc.
Ostensibly, we're taught to speak the Queen's English. For example, the 'a' in dance, bath, grass and Frances
is a long one. However, if you hear a Kiwi speak, you'll know we don't sound (generic/southern) 'English' when we say those words. There's much more of an 'aaaahh' sound when we say them.
It's a long A, but it's said in a Kiwi accent.
On the other hand, many Australians use a short A in words like dance, but maybe a longer A in, say, last. But again, it's a distinctive Aussie accent.
Oh, and Cockney is an accent...? Cockney rhyming slang is slang. Right....?!