Even with an invasion by the alien race known only as the 4-5-6, 'Torchwood: Children of Earth' could have fit neatly into Toobworld as a whole. So what if no other show ever depicts or even mentions the time when every child on Earth stopped in their tracks and began chanting "We. Are. Coming."? We could always say it happened off-screen for those other shows, at a time not depicted in their regular episodes.
And as for it never coming up in conversation between characters? Before 'All In The Family' came along, only a miniscule few of the American sitcoms during the sixties ever mentioned the war in Vietnam. It just wasn't front and center in their current concerns.
The same goes for ethnic cleansing in the 1990's and the War on Terror since 2001. Within Toobworld only, the same is true for any mentions of the Eugenics Wars outside the 'Star Trek' franchise.
Let's say the events that began in the original broadcast of the first episode of 'Torchwood: Children of Earth' were happening at the same time as the events in the episode of 'The Closer' which was broadcast at the same time (at least in the Eastern seaboard time zone). (The 'Torchwood' mini-series was broadcast first in the United Kingdom two weeks before its American premiere; thus, that's when it may have taken place*.) Nobody on that episode of 'The Closer' bothered with mentioning the fact that all of the kids in Los Angeles served as the vessel through which the 4-5-6 spoke. That's because they were too busy trying to solve the crime depicted in that particular episode.
*Since the events within 'Torchwood: Children of Earth' showed kids still in school, it was probably depicting what happened in Toobworld just a few weeks earlier, in June. If so, then in the correlating episode of 'The Closer' ("Blood Money"), the Major Crimes Squad was investigating a staged kidnapping. But again, they were too pre-occupied with that to be discussing the strange occurrence with the world's children.....
So to make a short story long, Toobworld could have absorbed the story of the 4-5-6 invasion into the world of Earth Prime-Time... if it weren't for the depiction of the Prime Minister as Brian Green instead of as Gordon Brown, who's the PM in both the Real World and in the main Toobworld.
At least one show with no reason to be banished from Earth Prime-Time has mentioned Gordon Brown as the Prime Minister - 'Outnumbered'. I wouldn't be surprised if his name has come up in dialogue on prime time soaps like 'EastEnders' and 'Coronation Street'. Since the so-called "reali-tv" show 'Dragon's Den' was depicted within an episode of 'The IT Crowd', I suppose it could be said that Gordon Brown has already joined the League of Themselves since he appeared in an episode of 'Dragon's Den'.
So with Gordon Brown established as the Prime Minister in Toobworld, does that mean Torchwood, along with 'Doctor Who' has to be banished to another TV dimension? (Jack Lord only knows 'Doctor Who' has given plenty of provocation in that regard since Russell T. Davies brought it back to life!)
It'll probably cause plenty of backache from bending over backwards to make it work, but I think I may have a splainin as to why the Prime Minister is Green, not Brown (in name, not skin color)......
After the events of the 'Doctor Who' two-parter "Aliens Of London" and "World War Three" (horrible episode titles in my opinion!), new emergency protocols were drafted. They were to be used during such a state emergency as an alien invasion. When the coming arrival of the 4-5-6 became imminent, those protocols were invoked. And one of them had the real Prime Minister - Gordon Brown - shuffled off to a secret location until the crisis was over. Such protocols have always been in place for the President of the United States as well in case the Cold War ever went critical.
However, a fake Prime Minister would then be put in place and the government would take emergency control of all TV, radio and newspaper sources so that the PM would be referred to as being this fictional figurehead - in this case, Brian Green. This would be done in order to deter the alien invaders from seeking out the true leader of the country.
If the 4-5-6 were monitoring the information output from Great Britain, they would see only mentions of Brian Green as the leader of that nation. We saw in 'Torchwood: Children Of Earth' examples of the military clamping down on a rebel TV news broadcast, so we can be assured that's what would happen if anybody tried to "blair" the truth about the Prime Minister. (blair/blare..... Sorry about that, Chief.)
The main function of this fictional Prime Minister would be to make sure that nothing could be traced back to 10 Downing Street in any official capacity, all the while serving as a sacrificial lamb in case the 4-5-6 did attack.
I don't know if Brian Green was the actual name of this pseudo-Prime Minister - I'm leaning towards the belief that it was - but his actions would be in the name of the real PM. And we'll see how that plays out over the course of the week.....
If it is a fake name, it could very well have been chosen because of the events depicted in that 'Doctor Who' story about the Clan Slitheen. The alien who assumed the duties of the Prime Minister, Jocrassa Fel Fotch Pasameer Day Slitheen, was disguised in the skin of a human MP, Joseph Green. Maybe this was either a tip of the hat in his memory, or a sick in-joke by whoever wrote up the new protocols..... What do you think? Is that a splainin that could work in this situation?