Captain Jack has an American accent. They are British because the TARDIS translates the language into what the companion/viewers understand. When translating to English, the default accent is British, for some reason.
*I walk up to the TARDIS and set a small glowing candle on the pavement* Goodbye my Impossible Girl. *I wipe the swelling up tears from my eyes with the back of my hand and I watch the new box in a sad gaze* <<<This is absolutely beautiful