David Cameron says that Russia’s annexation of Crimea ‘will not be recognised’. Ukraine’s Prime Minister Arseniy Yatsenyuk promises that ‘we will take our territory back’. They are both misguided. Let Crimea go: it will be the making of Ukraine and the end of Vladimir Putin. Without Crimea, there will never again be a pro-Moscow government in Kiev. Ukraine will have a chance to become a governable country — a strongly pro-European one with a Russian minority of around 15 per cent. Putin will have gained Crimea but lost Ukraine for ever. And without Ukraine, as former US national security adviser Zbigniew Brzezinski famously said, ‘Russia can no longer be an empire.’

Crimea is a gangrenous limb on Ukraine’s body politic. It will never be governable from Kiev again. What Ukraine needs now, after two decades of thievery and mismanagement, is a kamikaze government that will implement unpopular reforms — including amputating the Crimea.

The good news is that, thanks to Putin’s aggression, there is no shortage of wealthy western benefactors willing to nurse the amputee back to health. The European Union originally presented President Viktor Yanukovych with an Association Agreement that threatened to destroy Ukraine’s rust-belt economy in order to save it: unsurprisingly, Yanukovych went to Moscow for a better offer. But Yanukovych has been overthrown by people power, Ukraine’s new leaders are so serious about austerity that they flew economy class to meetings in Washington, and whatever government emerges from the May elections, there will be few pro-Moscow voices in it. With Crimea gone, Ukrainian politics will no longer be a tug of war between the Ukrainian west and the Russian east: the balance of power tips irrevocably west.

Thanks to Putin’s rash decision to occupy Crimea, not just the EU but its most powerful members — notably Germany, the UK, France and Poland — realise that supporting Ukraine is no longer about handouts but principle. Countries that strive towards European values — and suffer for it — should be rewarded and protected. Angela Merkel, the European leader who knows Putin best and is usually the most conciliatory towards Russia, told the Bundestag last week that he was ‘on a different planet’. Brussels has hurried to offer an amended Association Agreement; the US has backed a generous bailout from the International Monetary Fund.

Physically, the Crimea is easy enough to cut off: it is connected to Ukraine by a single, tiny neck of land to the north, and to Russia only by a slow ferry (though that will speedily be replaced, says Moscow, by a $3 billion bridge). The peninsula receives 80 per cent of its water and electricity from Ukraine; this year about $300 million of Crimea’s $540 million regional budget was due to come from Kiev. Its two main industries are tourism — mostly from Ukraine — and the Russian and Ukrainian navy bases in Sevastopol.

Russian media portrays Crimea rather as one would speak of a newly acquired ruin which could, one day, become an ideal family holiday home: it will replace Egypt as a tourist hotspot, predicts Russian Channel 1, and its offshore oil and gas reserves will cement Russia’s position as the world’s top energy producer. Crimea’s pro-Russian leader, Sergey Aksyonov — who before the latest crisis led a block of no more than 12 per cent of the regional government’s seats and has been accused of being an enforcer for the ‘Salem’ mafia gang with the nickname ‘Goblin’ — received 15 billion rubles ($410 million) in financial aid from Moscow after he signed the act of unification last week. But bank accounts in the territory remain frozen, locals are furiously buying all the dollars they can and tourism has ground to a halt.

Doubtless Putin will pour money into his acquisition, as he has done into Chechnya, South Ossetia and Abkhazia. But making Crimea a viable part of the Russian Federation will be cripplingly expensive. ‘Today, our Crimea looks no better than Palestine’ — not the words of a EuroMaidan enthusiast in Kiev but of Russia’s regional development minister, Igor Slyunayev, speaking to the Russian business daily Kommersant just before Putin’s Anschluss.

What’s more, in taking Crimea Putin has made himself a hostage to Kiev. Putin’s main economic leverage is that he sits on Ukraine’s gas pipelines: but now Kiev sits on Crimea’s road, rail, water and power. And unlike the gas wars that the Kremlin launched against Ukraine in 2005 and 2009, which cut off Moscow’s European customers, a Ukrainian blockade of Crimea will hurt only Crimeans.

Donetsk — or as it was known until 1961, Stalino Province — remains a problem for the revolutionary government in Kiev. Russian-backed protesters and imported provocateurs are vocal and violent. But they are in a minority. According to the last census in 2001, ethnic Ukrainians account for 57 per cent of the population, Russians only 38 per cent.

But Putin’s biggest problem is not that annexing Crimea will be expensive for the treasury — it is that it will be expensive for Russia’s elite. On the face of it, US and EU sanctions amount to a mere pinprick. But the cost to Russia’s business class will be deep, and come in subtler ways — higher borrowing costs, evaporated international enthusiasm for their share offerings, a sliding stock market, a weak ruble, bad credit ratings. With energy prices sliding too, and Europe pushing hard to find alternatives to Gazprom, Putin is strangling the goose that laid golden eggs in pursuit of an incoherent imperial vision. Russia’s moneyed class will not forgive him.

For the first time in years Russia stands absolutely isolated in the UN Security Council, abandoned even by its old ally China. And former Soviet countries with large ethnic Russian populations — Kazakhstan, Uzbekistan, Belarus, Latvia — are all suddenly more nervous. Hitherto, the price of their loyalty has been cheap Russian gas. That price will soon go up. The foundations of Putin’s post-Soviet Customs Union have been shaken.

Putin says that Crimea has ‘always’ been part of Russia. He is right — in the sense that, like Warsaw and Vilnius, it was annexed to the Russian empire under Catherine the Great. But now Poland’s defence ministry has announced it will relaunch plans to establish a joint Polish, Ukrainian and Lithuanian military brigade, the first step towards Nato membership. In Crimea, Putin has scored the ultimate Pyrrhic victory.