Leela spoke like that long before she met the Doctor, and he was the first Gallifreyan she ever met. She did later spend decades living on Gallifrey (originally with her husband Andred, later as Romana's bodyguard), it didn't change her speech much.
Behind the scenes, this was meant to reflect the fact that she came from a primitive and degenerate tribe.
In-universe, it could be explained by the computer Xoanon deliberately trying to divide the tribe into two species. Gradually splitting their language would be a good way to do it. (Especially since it came to believe that it was a god--think of the Tower of Babel story.)
Also, most people on the show are often not speaking English. When the Doctor talks with an English (or Scottish, American, Australian, etc.) companion, they probably are speaking English. But when he talks with some alien like the Foamasi, the TARDIS translates everything--he hears Gallifreyan, they hear Foamasi, and presumably we hear English.