It's been subtle, but there were more hints at Torchwood's connection to the UK's government in Doctor Who than on the actual Torchwood show. Harriet Jones said she wasn't supposed to know they exist, meaning it's an organization so secret that the Prime Minister can't know about it. So it's not your typical intelligence/black ops group.
I had the impression that Torchwood was controlled by the royal family moreso than the British government. Queen Victoria founded the organization during a time where the queen was, not unlike today, just a figurehead whose power was surrendered to the PM and Parliament. The queen controlled Torchwood, but the PM and Parliament didn't.
Not to mention Yvonne (the head of Torchwood from Doctor Who's series 2 finale) said Torchwood's duty was to the British Empire, which no longer exists as far as anyone knows. That sorta implies that Torchwood was operating out of some secret agenda to restore imperial power the the UK, likely to the royal family again.
But that's just me speculating. In the end, with the Cardiff branch apparently being the only one still standing, Jack has completely reorganized them for a new, more altruistic purpose.