The American eagle swoops a little closer to the growling Russian bear. Tensions mount between Washington and Moscow. Russian diplomats are expelled by the US president.

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Is this a second cold war? No: it is the first hotdesk war. Its soldiers can work anywhere, on laptops, in internet cafes, or in the heart of the Russian intelligence establishment. Their weapons are bytes, not bullets. Their mushroom cloud is digital chaos.

This is Theresa May’s first full-blooded geopolitical challenge (Brexit was part of her inheritance). To date, Barack Obama has responded to Russia’s cyber-attacks during the US presidential election with a range of sanctions; Vladimir Putin has declined, for transparently tactical reasons, to retaliate; and Donald Trump has taken to Twitter to praise the Russian president’s decision as “very smart!” (Isn’t there something especially pleading about that exclamation mark?)

The prime minister must now decide how to position herself in this spaghetti western standoff between the Good, the Mad and the Fugly. She could do nothing, of course. But that would be a craven lapse into paralysis, given the manner in which she has handled Putin in recent months. In October she accused Russian forces of “sickening atrocities” in Aleppo, and undertook to send 800 troops to Estonia, one of four Nato battalions dispatched to deter Russian aggression.

In November, the prime minister declared that the west needed to “keep up the pressure on Russia” over its conduct in Syria. Meanwhile, she authorised the transfer to Estonia of high-precision long-range missiles to be deployed alongside drones, tanks and RAF jets. I doubt that May ever believed Putin could be driven out of Syria. But the buildup of forces in the Baltics is an unambiguous warning to him not to push his luck.

She knows too that conventional warfare is but the half of it. As Andrew Parker, director-general of MI5, said in his Guardian interview last year, Russia “is using its whole range of state organs and powers to push its foreign policy abroad in increasingly aggressive ways – involving propaganda, espionage, subversion and cyber-attacks. Russia is at work across Europe and in the UK today.”

In this context, May can hardly now pick up the pom-poms and join Trump on the cheerleading mat. And just to remove any doubt, her allies are categorical that there will be no strategic shift in response to a single tweet by the president-elect. As a starter, she indicated over the weekend that Russian oligarchs with links to Putin would no longer be welcome at Tory fundraising events – hardly a dagger in Moscow’s flesh, but a clear enough indication that she has no intention of following Trump down the road of appeasement.

Still, he is going to be president in less than three weeks. It is central to the prime minister’s vision of Britain’s place in a post-Brexit world that the “special relationship” should survive and prosper, especially in the form of a new bilateral trade deal. Her allies were delighted that Trump raised the precedent of Ronald Reagan’s bond with Margaret Thatcher in his first phone call with May.

To be fair, they are realistic: nobody knows how the 45th president will respond to the counsel and promptings of his foreign counterparts. But Team May is determined at least to try. Aside from the prime minister’s forthcoming visit to Washington, there are plans for senior No 10 staff to make a separate trip to meet their opposite numbers in the new White House.

The specific conundrum May faces is that the standoff between Russia and the US is (apparently) about to yield place to a love-in. The greater threat in the era of Trump and Putin is not conflict but convergence – and not a convergence of peace, but a new struggle on many fronts, within and between nations, in which Russia and the US are on the same side.

Already, one can see the lineaments of that struggle: internationalists versus nativists; autocracy versus liberalism; traditionalism versus pluralism. It is fast rendering obsolete the old matrix of left-right, and east versus west. Trump and Putin are very different politicians. One is a tycoon and television star; the other a pitiless product of the KGB. But in this newly ordered world they are potential allies – of the worst sort.

May’s priority must be to dash any hopes the president-elect may have that Britain will be a wholly compliant Airstrip One

How chilling are the resonances with Nineteen Eighty-Four – and particularly the passages from “The Theory and Practice of Oligarchical Collectivism” read by Winston Smith. This text describes a world in which great geopolitical blocs are “not divided by any genuine ideological difference”, in which “the fighting, when there is any, takes place on the vague frontiers whose whereabouts the average man can only guess at”, and in which the “cultural integrity” of each bloc is its true priority. From this fictional warning, it is not such a great leap to Trump’s Oceania and Putin’s Eurasia.

To persist with the metaphor, May’s priority must be to dash any hopes the president-elect may have that Britain will be a wholly compliant Airstrip One. In this respect, she faces a more nuanced diplomatic challenge than confronted, say, Thatcher or Tony Blair. Reagan and his “dear friend, Margaret” agreed on practically everything. Blair and George W Bush were from different sides of the political divide, but discovered common ground after 9/11.

It is self-evident that Trump and the prime minister do not enjoy any such identity of conviction. Yes, they are conservatives who share a core belief in the primacy of the nation-state. But on Nato, protectionism, climate change, Islam and much else, they differ fundamentally. May’s mission is to find common ground without selling out. It is a task of spectacular complexity.

On Russia, however, she cannot budge an inch. Her task as the only G8 leader in Europe not facing an election in the next 18 months is to confront Trump with the ineluctable facts about Putin: that he is an inveterate regional aggressor, a globally active enemy of democracy, and a mostly unchecked threat to the stability of the west. That his campaign of cyberwarfare alone mandates those nations he has targeted to enact further sanctions – and not only the symbolic kind.

Somebody needs to tell the president-elect that his political crush on Putin, as well as dividing his own party and country, and splitting the west, will send the worst possible signal to an autocrat just waiting for the green light. As the Iron Lady once said: this is no time to go wobbly.