Set within the Shadow Proclamation.

The Human Affairs department represents all those worlds of Human descent, colonies or ancestral origins. ie (not just those on Earth.)

The rough timeline is set after Stolen Earth, where Earth, Sol System is still a closed planet as it has not had fully recognised First Contact (although there is nothing to suggest that various Earth authorities such as Torchwood, UNIT etc are not unaware of their presence. There is a small hint of this during DH2 after Megan has broadcast Code 666 - the Armageddon Code.)

Regardless of this, the Shadow Proclamation have still dealt with problems arising throughout Earth History - although this would not have been obvious to the people concerned.

It is not unusual for them to send their various police to deal with criminals and offenders on behalf of other species (ie Judoon - Smith & Jones) for example.

Usually they will try to deal with complaints and investigations without trying to draw too much attention to a closed planet.

The Human Affairs department (which goes beyond just the Investigative Team) includes displaced 'Humans' from Earth itself from both past and future.

Examples include descendants from Atlantis, who were rescued from the cataclysmic destruction of their continent, some who were abducted by non-terrestrial beings and abandoned thereafter and individuals who have merely drifted through time and space either by accident or through their own volition.

I've based this roughly using Russell T. Davies' original scripts and ideas for Stolen Earth (ref Writers Tale) where Midshipman Frame was going to turn up as a Shadow Soldier - which would have placed it sometime after Voyage of the Damned.)