I've worked out a lot of details about the history of Pete's World, namely that the divergence happened with the fact that the Doctor and Rose weren't there to prevent the werewolf attack on Queen Victoria. She shot herself rather than let it take her, and both the People's Republic and Torchwood were born in the rather chaotic aftermath.

Torchwood didn't have the unofficial government sponsorship, but the Republic did take over some time later (as Jake notes in either AoG or DD, I forget which).

How that would affect Pete ... interesting.