There is also no 'British' dialect. English/Welsh/Scottish/Irish, unless you are saying that Londoners sound the same as Edinburghians, Cardiffians and/or Derrites. And even then, the Northern/Southern/West Country/Midlands groups in England are very, very different! You could say British English, but that's not a dialect, per se, more of a general (written-only) similarity between the dialects of the UK, such as vocabulary and grammar. British English is British English, not British-dialect English. Similarily, American English is not a dialect either, for much the same reasons - Bostonions don't sound the same as Angelenos who are quite different from Texans. It's not as pronounced as the British Isles, owing the the much shorter period of linguistic change that the US has had, but it's still there - it's more noticeable in the more remote populations, such as the Appalachians. Dialect is a fairly 'small' grouping, linguistically.
The biggest divide in British English, and the one most familiar to people around the world, is Upper- and Lower-class English (a sociolect)- Upper-class English has much less regional variation compared to Lower-class English, for various reasons, primarily education that reinforced a specific way of speaking; they're often used as the dialect of choice for villains, for some reason.
Accent is different - that's when it's just pronunciation (and maybe small amounts of vocabulary and grammar, but 95% pronunciation)
But then again, this is all coming from a linguistics background, take that for what it may.
And also, Teetoku-chan's always been upper-class English in my mind. More formal and suchlike; hence, her idolect is that of a Upper-class English lady. But not super English. Like, 30-40% toff - all sound and fury with little to back it up. This comes from her use of the copula ～のじゃ, which is a semi-archaic form of the 'standard' copula だ。 This doesn't translate directly into English well, so I default to the 'standard old-timey formal' style, viz. Upper-class English. Plus, it fits with the character nicely.
TL;DR British English is not a dialect, but it has lots of dialects in it. I gave Teetoku-chan an Upper-class English dialect/accent, to account for the ～のじゃs at the end.
