Our heroes have found a chemical plant. In the chemical plant they also a cache of weapons left over from the war. Between Kerry's chemistry degree and Sooty's old experiments with explosives (back in the days when she was reading The Anarchist's Cookbook and other similar titles), they manage to arm themselves with guns and some home-made devices (explosives, smoke bombs, poison gas, bottles of acid, etc).
They also find underground tunnels that lead them to some good strategic points, where they find the alien spacecraft, and are able to observe what is going on. Basically, the aliens have enslaved the inhabitants they have encountered, and are using them as a labor pool to gather materials (I don't know what they are mining - possibly trashpicking the radioactive sites for valuables?). With some careful planning, some booby-traps, and Brian's magic, the three launch a successful assault against the aliens, killing a number of them, and routing the rest of them. The aliens retreat to their spaceship and take off. Brian and Sooty manage to stow aboard, leaving Kerry behind to free the slaves and to tell the story. Brian and Sooty are going to destroy the ship.
Why the two of them? Because Brian has the power to do massive damage to critical parts of the ship (like the reactor core) but would have no clue how to tell the reactor core from the holodeck. Sooty has been a grease monkey since she was a kid, and has a good instinctual understanding of how things are put together.
So the two of them get onto the ship, hide out, explore, find the right systems to sabotague. Brian puts Sooty in a life pod and launches her into space, then blows up the ship. He manages to get into a life pod before the thing blows, but doesn't have time to get away. His magic is strong enough to protect the interior of the pod, but it's propulsion systems are destroyed and he drifts aimlessly through space until the Starbucket's improbability drive puts it directly in Brian's pod's trajectory.
Which is where the story "The Mission" picks up.