Children of Men takes place in the Half-Life universe.
Britain is not the only country with a functioning government.
The sterility plague was not caused by nuclear fallout.If it were, humans would not be the only species affected, yet we see many animals (cats, dogs, chickens) that have much shorter lifespans than 18 years. Whatever caused it specifically affected only humans.
The government of Britain is mostly comprised of reasonable authority figures.Many oppressive governments have tried to scare their people into believing the world is falling apart, and that the only reasonable course of action is to bear down to keep the outside from coming in so citizens can live in peace. What if it wasn't fiction, but the God's honest truth? How would a good government respond to a world that has actually gone to Hell in a hand-basket? The British government may simply be doing the best it can to hold things together, driven to brutality in the attempt to preserve what semblance of civilization remains.
England has identified the source of the fertility plague and it is communicableHence why they are trying to get the fugitives out of the country or destroy them. They want to do so before releasing the cure.
The sterility plague is wearing offShe was just one of the first.
Children of Men is a sequel to the movie Rise of the Planet of the Apes.The virus from Rise mutates so it is not so virulent and deadly, it merely removed reproductive ability. While the human race slowly exits (or at least far fewer are reproducing for now), the apes experience a great birth rate.