A technical fault on the bus has stranded Iris and Panda in early 1970s London. Iris has been spending her time doing odd jobs for MIAOW, and she is sent to investigate when Professor Trevor Ramsbottom and his assistant Audrey discover something strange beneath an Underground station: oddly-shaped skulls and a china tea set that, according to Audrey, reeks of evil. The public are clamouring for the Tube to be reopened, and Professor Ramsbottom calls a press conference in the hope of convincing everyone to leave him alonew hile he works; however, Audrey spoils his plans by blurting out that they have found things that should not exist. Ramsbottom calls an end to the conference, but Iris uses her MIAOW credentials to force her way into the investigation. The Professor reluctantly invites her and Panda back to his laboratory beneath the South Bank Complex, where Panda tries to chat up Audrey despite being aggressively uninterested in her tales of the wild adventures she's had with Ramsbottom.

Instead of returning to their secret HQ above a bus depot and pool hall in Newcross, Iris takes Panda back to the Underground station to investigate further. Rather than just destroy the anomaly as MIAOW would no doubt prefer, she intends to expose the heart of the problem using a logic bomb, an illegal device that exposes the presence of implausibility but tends to set ludicrous events in motion as a side-effect. The bomb exposes a bright green burrowing machine buried beneath the earth and labelled "Jabberwocky" in gothic script. Ramsbottom calls in the Special Forces to unearth the rest of the ship, but while they are doing so, a soldier is knocked senseless by falling debris and begins to chant a nonsensical children's rhyme. The drills then break through the hull of the ship, and Iris and Panda enter to find that it's occupied -- by the White Rabbit and Mock Turtle out of Alice's Adventures in Wonderland.

Iris takes the sight in stride and welcomes the characters to London, but they're clearly terrified and upset to find themselves in the year 1973. The Professor and Audrey can't believe that the creatures really are characters from a 19th-century novel come to life, but all the tests they can think of indicate that this is indeed the case; the Mock Turtle's veins really are full of oxtail soup, and the Jabberwocky, despite its advanced construction, nevertheless seems to have been constructed in the 19th century. The White Rabbit and Mock Turtle claim to have been escaping from something, but they don't want to talk about it; however, they do reveal that the skeleton and tea service that the Professor and Audrey unearthed are all that remains of the Mad Hatter, who tried to flee when the ship first arrived but was caught in the molten slag outside.

Iris spends several days and nights trying to repair the Jabberwocky. Panda is surprised by her determination and focus, and she eventually admits that the reason they're stuck in this time period is because the bus has been sabotaged. Iris grew up in the slums of the Clockworks, a place of logic and reason; even when she got out of the slums she found the Clockworks too snobbish and uptight to satisfy her, which is why she stole the bus and fled to explore the Universe. The Clockworks have caught up with her and damaged the bus to keep her trapped in the 1970s; but if Wonderland is real, it could be her ticket out, as the magic of that world would be against everything the Clockworks stand for.

The White Rabbit and Mock Turtle have become media celebrities, and in a TV interview, the Mock Turtle reveals that they hibernated inside the Jabberwocky for 100 years after their escape. However, the White Rabbit is still wary of surface dwellers and warns the Mock Turtle against revealing too much. A real life jabberwocky then emerges from the Underground station and begins killing people on the street; despite the danger, however, Iris is upset when the military shoot it dead. Convinced that MIAOW just wants rid of all fabulous creatures, Iris sends Audrey to fetch the White Rabbit and Mock Turtle to safety, intending to drive her bus down the tunnel that the Jabberwocky machine dug up from the centre of the Earth. Audrey ushers the terrified Mock Turtle and White Rabbit into a taxi with herself and the Professor, but as they drive off, she reveals that she's not really the timid little assistant that Ramsbottom had believed. She's an undercover agent for MIAOW, and after every adventure she's shared with the Professor, she's secretly destroyed and killed all evidence of their fantastic discoveries so as not to upset the status quo. The taxi driver is also a MIAOW agent, and he's taking Ramsbottom and the Wonderland creatures to MIAOW headquarters, the Pussy Parlour, to dispose of them.

Upset by Audrey's betrayal, the Professor betrays his own principles by hitting a woman. In the ensuing confusion, the taxi crashes, and Audrey, the White Rabbit, and the taxi driver are all killed. Ramsbottom gets away with the Mock Turtle and phones Iris, warning her that MIAOW will be coming for her next. Iris, who only started working for them to access the alien technology she believed they were hoarding, decides to part company with them for good. She drives to the Underground station, and Panda lobs the remaining logic bombs into the tunnel that the Jabberwocky machine dug up from Wonderland. He and Iris drive down the rabbit hole, through magma, corridors of rock cluttered with Victorian bric-a-brac, and bizarre psychedelic hallucinations that don't come across fully on audio. As they drive, an image of the Mock Turtle appears on the bus's windscreen; he's using the power of the concentrated oxtail soup in his veins to communicate telepathically and warn Iris and Panda that MIAOW is willing to kill them both to prevent them from bringing the nonsense of Wonderland up to the surface world. Either this adventure is becoming curiouser and curiouser, or Iris and Panda have spent so much time in the company of Wonderlanders that they've become infected by their nonsense.

The bus crashes out of the tunnels, through a tree, and onto the ground of Wonderland. The sky is lilac, the atmosphere is creepier than Panda had expected, and in the distance is the scarlet palace of the Queen of Hearts. A cat materialises before their eyes -- not a grinning Cheshire Cat, but a dour Salford Cat. After they bribe it with a slightly melted Curly Wurly, it reveals that Harriet Dodd -- a brilliant but mad scientist from the Victorian era, and a noted landscape gardener -- is waiting for them at the other end of Wonderland. Harriet was one of the earliest members of MIAOW, and she created Wonderland as a prison for fantastical creatures from other dimensions. The Cat vanishes again, warning Iris and Panda that they too will soon be trapped in Harriet's zoo of freaks. They nevertheless have little choice but to drive onwards, through terrifying hordes of albino bat babies, bread-and-butterflies the size of the bus, and, most terrifying of all, the ghosts of empty bottles of booze.

Harriet Dodd is the Queen of Hearts, and her enormous head contains five brains: her own and the brains of her four genius assistants, which she removed and placed in a specially designed skull so she could tap into their intellects. As she and her Dodo servant prepare to receive their first visitors in over a century, a metafictional discursive glitch enables her to hear Panda narrating this story from the future. Before the glitch corrects itself, Panda warns Harriet that MIAOW are coming for her. Indeed, Audrey survived the car crash after all, and has used the Jabberwocky machine to follow Iris's trail into Wonderland. Professor Ramsbottom and the Mock Turtle watch in horror as MIAOW's woman stormtroopers spread out with flamethrowers to prevent Wonderland's influence from spreading; it was created in the 19th century as a prison in which subversive elements could be contained and studied, but contemporary MIAOW simply wants all such silliness destroyed. Wonderland seems to be dying in advance of the MIAOW warriors, as if it knows that it's coming to an end, but the Professor, deeply disappointed by Audrey's betrayal, helps the Mock Turtle to overpower her and seize control of the Jabberwocky machine.

The Salford Cat materialises on the bus and guides Iris into Harriet Dodd's palace, where Harriet concedes that the White Rabbit, Mock Turtle, and Mad Hatter fled from Wonderland because she used to be quite, quite mad. However, she claims to have mellowed, and reveals that she summoned Iris here in a roundabout manner because only Iris can save Wonderland. Harriet joined MIAOW after she was shunned by the Victorian scientific establishment, and they helped her to create Wonderland because they hoped to get something out of it themselves. Now, however, they simply wish to destroy it all. Harriet dreamed Wonderland into existence using a feasibility generator, a device that makes the impossible more probable and counteracts the repressive desires of those who wish to make sense of things; Wonderland is here now because MIAOW woke Harriet up in order to get to Wonderland and destroy it, and the environment is darker and more dangerous than Iris expected because Harriet knows these are Wonderland's final days. At Harriet's command, Dodo transforms back into the feasibility generator, and Harriet orders Iris to fix her bus with it; once the generator has become part of her bus's workings, it will spread absurdity wherever it goes, and a bit of Wonderland will survive in Iris.