The TARDIS materializes in a jungle. At first, the travellers think they’re on Earth, but the flora and fauna are from every continent, and there is a metal ceiling. The Doctor realizes they are on a vast spaceship. Dodo sneezes; she has a cold.
At first, they see strange amphibian-like one-eyed creatures which they learn are the Monoids, who came to Earth centuries ago as refugees, but there are humans as well, including millions in microscopic size in suspended animation—the last remnants of humanity. It is ten million years in the future, and Earth is about to be destroyed by the swelling Sun. The Ark is headed for the planet Refusis II, where it will arrive in another 700 years. The time-travellers see a monumental statue of a human being, which the voyagers are carving as a group project.
Dodo’s cold spreads and proves to be fatal to both races. At first, the Tardis crew is to be executed for this, but they are given a laboratory to work out a cure, which they do. Before the TARDIS leaves, they watch the destruction of Earth on the long-range scanner.
Seven hundred years later, the TARDIS materializes again. The statue is now of a Monoid. It seems the Monoids have rebelled and seized the ship. The humans are slaves. As soon as the Monoids have landed on Refusis, the Ark is to be blown up and all the humans killed.
The Doctor and Dodo, however, are to descend in the first landing craft, as hostages for Steven’s good behaviour, after he tried to foment rebellion. Refusis turns out to be inhabited by invisible creatures who react badly to the Monoids’ autocratic and violent ways. In the end, they accept the immigration of both races as long as they remain peaceful. The time-travellers return to the TARDIS, but The Doctor becomes invisible.
The Monoids are a bit silly, with flippers for feet, fright-wigs, and masks with roving ping-pong-ball eyeballs held in the actors’ mouths, but the science-fiction story is interesting, if a bit derivative of several H.G. Wells stories. But then, pretty much everything in SF can be traced back to Wells, Verne, and Burroughs.