London accent?

If I had a character with a London accent, is that specific enough or should the location be more specific? This is set almost 80 years in the future and the character isn't from London. She's American but displays a British persona as part of her working personality. Actually I'm now thinking she should go all out on the hokey end and sound almost like a Dicken's orphan out of Oliver Twist. I'm basing her on Pee Wee Herman, not that her character is like his but that her put-on-persona is that fake, everyone knows it's a gag.