The Black Corridor - a stand-alone novel from 1969 by Michael Moorcock. isfdb.org notes that Hilary Bailey (his wife at the time) is an uncredited co-author. Here's the flap-copy from the first hardcover, which gives a reasonable summary or set-up:

The spaceship Hope Dempsey held thirteen men and women, refugees fleeing an Earth doomed by atomic destruction. While twelve slept in suspended animation, the thirteenth, Ryan, ran the ship alone. For three years he had been responsible for the lives of the only humans left in the universe.

Ryn's job was to see that they reached a distant sun where unmanned probes had detected two Earth-like planets. As he checked the life-support systems and read the ship's computer printouts, his thoughts and dreams often turned to the Earth he hadn't seen for three years, since their take-off in 2002. It was still hard to believe that society had collapsed so quickly. A massive wave of nationalism had swept across the globe leaving thousands of tiny states and kingdoms in its wake. Nothing could have stopped the coming holocaust.

But Ryan had been determined to survive, and with the ruthless ferocity of a wolf he had fought, bribed and murdered his way to the Siberian Plains with his small group. There man's only project for reaching the stars had rested on its launching pad for two years. Seizing the ship, Ryan and his people had barely escaped into the cold sanctuary of space.

The ship had performed magnificently, but, almost three light years from Earth, the awful loneliness of Ryan's task began to catch up with him . . . and he was haunted by strangely indefinable fears. Slowly a crisis was developing on board ship, and Ryan realized that even this last remnant of human life was threatened with extinction, in the lonely dark corridor between stars.