It’s the near future, and Europe has closed its borders firmly to refugees. A vast permanent camp has grown in sub-Saharan Africa, sustained (just) by western aid. But its inhabitants are stuck: even those who are able to earn find it pointless to save. The prices charged by people-smugglers are going up faster than the refugees can make money, and the days of risking it all in a dinghy on the Mediterranean are long gone.

That’s the premise of Timur Vermes’s hefty new novel, and what sets the action off is the arrival of an airhead German reality TV star, Nadeche Hackenbusch, who flies to the camp to film a series of her show, Angel in Adversity. She arrives with a personal makeup artist, a pink zebra-striped car and a supply of her line of Hackenpush-up bras to hand out to the needy. There she meets “Lionel” (so named by the TV people after he says something mystic-sounding about lions), a young refugee recruited as her on-camera fixer and shortly afterwards as her lover. Their romance is tracked by a compliant journalist called Astrid who files copy like this:

One is instinctively reminded of War and Peace, that wonderfully profound novel by Leonardo Tolstoy: a young noblewoman, played by the unforgettable Audrey Hepburn, finds her great love, and this in the midst of hardship and in Russia. But when one points out this striking comparison to Nadeche Hackenbusch, and tells her that over the past days and months she has truly become an Audrey Hepburn of hearts, she just laughs modestly and reaches for the hand of Lionel, her new Bolkonsky, a man as good-looking as he is mysterious.

We are in the territory of what sometimes gets called “broad satire” – broad enough, in this case, that it could comfortably accommodate an eight-lane autobahn. Nadeche is a preening nitwit; Astrid is a semi-literate fluff merchant with fatuous literary pretensions; their superiors are careerist stooges. Back home we’re introduced to a politician identified only as “the under-secretary” – whose boss, the minister of the interior, is first to clock that a TV star turning the eyes and compassion of the nation on a refugee camp might mean trouble.

And trouble it does mean. Lionel is no dummy. He has a smart idea and swiftly brings Nadeche on board: what if he and his fellow refugees – 150,000 of them – simply walked to Germany? The interior ministry is right to be anxious: “This isn’t just a mass of refugees perishing somewhere. This is a mass of refugees with their own telly programme. Presented by Nadeche Hackenbusch. It’s wiping the floor with the daily soaps.”

Where Vermes unexpectedly excels – compensating for his cursory characterisation and rather laboured ironies – is in thinking so ingeniously about the logistics of how all this might actually work. Lionel enlists the help of the camp’s chief mobster to arrange trucks of water and food to accompany the marchers, all funded by daily micropayments from their mobile phones. The detail becomes rather fascinating – and the initially slightly sluggish pace of the book picks up as it goes on.

As the column of refugees makes its way north, at a steady nine miles a day, that TV audience starts to have an effect on domestic politics. The far right – in a country with actual Nazis still uncomfortably close in memory – surges in popularity. There are demonstrations: “Don’t give them money and soya flour! We need a wall and firepower!” (That couplet, incidentally, gives a sense of how able and idiomatic Jamie Bulloch’s translation is, and I’d love to know what the German words translated as “shitgibbon” and “jizztrumpet” were.)

What are the politicians going to do? Borders in Africa and then the Middle East seem to present no obstacle, a handful of low-paid guards with sidearms being in no position to turn back 150,000 people, even if not easily bribed. Plus, since their avowed destination is Germany, and they carry their own resources, isn’t the easiest thing for each government to grant them safe passage – and perhaps offload a few of the country’s own refugees while they’re at it?

Steadily, the column of marchers advances and grows. So does its audience. The prospect that nearly half a million people are going to show up at the German border becomes a real one. Can they be bought off? Sabotaged? Mowed down? Can a fence be built? Electrified? And how will all this play with the folks back home? The novel starts to acquire a deeply involving game-theoretical aspect, along with a flavour of Ben Elton’s ingenious and underrated novel Popcorn, which also explores how being televised can make a tricky situation much trickier.

You get the sense that Vermes didn’t know quite how to tie it all up, but tie it up he does, and with whizz-bang energy and gleeful imaginative savagery. His achievement is to make this exodus, and the shaming hypocrisy of western reactions towards it, seem altogether plausible.

• The Hungry and the Fat by Timur Vermes, translated by Jamie Bulloch, is published by MacLehose (RRP £16.99). To order a copy go to guardianbookshop.com. Free UK p&p over £15.