There is, of course the theme of the world stopping having children based on a flu outbreak, but watching it again my wife noticed something else.
The film was released in 2006, so obviously made prior to that, but the Theo character was wearing a sweatshirt with 'London 2012' olympics on it.
Obviously the first thought is that they would have known about the olympic schedule at the time, but considering the theme of the film and the satanic ritual that was the opening ceremony I thought it was worth a mention.
https://www.kahramangiller.com/wp-content/uploads/2016/02/ChildrenOfMenPic.jpg
This film was set in the UK which means the movie is set about 15 years after the games. Keep in mind that the Olympics were awarded to London in 2005, Likely before filming started on "Children of Men." They must have knew about the plans for the Opening Ceremony during the bid process which meant that Danny Boyle was told to produce the ceremony the way the Powers that be wanted it to be done. The only thing they didn't factor into the equation was Hillary losing the 2016 election.