We need to remember that the grim dystopian world of nuclear warfare and its terrible aftermath that is described for us in this book is based on a hypothetical situation. What would actually happen to the world after a nuclear holocaust is a topic that was and continues to be fiercely contested, but particularly so in the era in which Shute was writing. The Cold War dominated life to such an extent and with brinkmanship being played between the USA and USSR it was clear that the end of the world because of nuclear warfare was a definite possibility.
Shute was therefore trying to work with hypothetical possibilities that were the result of a lack of knowledge and experience of nuclear weapons and warfare. I am sure some scientists would argue that the idea of having a nuclear cloud looming over the earth and travelling around the world might be problematic, but at the same time it is important to remember that, to take a modern day example, ash clouds from volcanoes are able to disrupt aircraft and traffic between different nations. Clearly we need to take this literary device as being a possibility of what could happen rather than something that is a scientific fact. Obviouisly, even if there was mass nuclear warfare, we would be unable to be around to see what would happen!