Except that the book could have the subtitle "The greatest giving up story ever told".
First, the scenario of spiked nukes is not technically accurate; you'd need as much cobalt as we mine in 100 years to achieve that type of effect.
Second, even if the radioactive cobalt poisoned the lands, it would have done nothing to the oceans. Oceans contain billions of tons of uranium for example. But it's too dilute. A few thousand tons of cobalt would have not moved any needle.
So, you have a nuclear submarine and some other naval assets. It could have been a great Noah's ark story. But Nevil Shute was not interested in a Noah's ark story, he was interested in the story where there is no human alive after a nuclear war. Science be damned. I simply could not read the last 50 pages or so.