One reason to imagine that Theresa May has hidden depths is that the thought of the country’s future depending on the visible portion of her ability is so alarming. These are unsettled times, so there is comfort in the idea of a prime minister with a plan – any plan. There is a psychological incentive to suppose that May thinks beyond the end of the day; that her strategy for Brexit is more sophisticated than it looks. Because it looks like deferral of hard choices, evasion of confrontation, and Hail Mary hope that something will turn up.

May’s starchy manner helps cultivate belief in an invisible realm of calculation. Inscrutability looks enigmatic. Her rigid persona seems to invite speculation that there is another, more versatile person behind the mask. It is hard to believe that what you see on screen is really what you’d get off camera.

It is not just in this country that observers crave access to a more candid version of the prime minister. During May’s first year in Downing Street, European Union politicians routinely asked their contacts in London for insight into the real Brexit plan. It seemed implausible that a serious country with a reputation for pragmatism would go about such a dangerous enterprise in such a haphazard fashion. It took a while for the message to get through that the appearance of improvisation and unreadiness was not an illusion.

May’s continental counterparts were also disoriented by the discovery that she can be as robotic in private as she is on screen. EU diplomatic channels hum with gossip about the British prime minister’s inability to drop the soundbites and slip into something more vernacular. She squanders precious top-level bilateral meetings by sticking to pre-briefed scripts. Angela Merkel, the German chancellor, and Mark Rutte, the Dutch prime minister, are two of Britain’s potential friends who have come away from talks with May stunned and frustrated, having learned nothing more than they might glean by watching her on television.

‘May’s starchy manner helps cultivate belief in an invisible realm of calculation. Inscrutability looks enigmatic.’ Photograph: Leon Neal/Getty Images

And May appears not fully to grasp that, in the absence of meaningful private dialogue, EU leaders study her public declarations for clues. Her speech to the Conservative party conference in September 2016 was written entirely for domestic, Eurosceptic consumption. Newly elevated to the Tory leadership, May felt she had to scour away any residue of remain support from her person. So she signalled a hard Brexit – outside the single market and beyond European court jurisdiction.

But the speech was read in EU capitals, and the conclusion drawn that the UK was aiming for severe detachment, on a model akin to Canada’s free trade deal. That was the logical extrapolation from the red lines May had drawn. When British diplomats told her that her speech was being interpreted as a recipe for “Canada dry”, she was shocked, telling mandarins that no such decisions had been made. How had the Europeans got the wrong end of the stick? Well, Prime Minister, that was the only end they could see.

It is normal for MPs to feel shut out from their leader’s inner circle. The problem with May is that there isn’t one

Diplomatic illiteracy is the defining pathology of May’s leadership. It infects her party management as badly as it impedes progress in Brussels. Although it is impossible to satisfy the pro-European and Brexit-ultra wings of the Conservatives at the same time, May manages to leave both sides feeling wounded and deceived, while also alienating the vital group in the middle who don’t care about technicalities and just want the job done.

It is normal for MPs to feel shut out from their leader’s inner circle. The problem with May is that there isn’t really an inner circle. MPs don’t know whom to approach for a steer on the prime minister’s instincts, nor whom to lobby for influence. It is striking how even ministers who have worked at close quarters with her through periods of extreme stress – the kind of circumstances in which camaraderie usually flourishes – admit ignorance of what really makes her tick.

This is not a question of “hinterland” – Denis Healey’s phrase for the colourful, textured region of a politician’s life beyond Westminster’s arid plains. Brexit would not be going any better if May could play the banjo. The missing element is something more central to political effectiveness. It is the mode for communicating on a wavelength somewhere between total secrecy and public performance. It is the “off-record” idiom that invites confidence and lubricates deals.

I’m not talking about whispered briefings to lobby journalists, which are usually transmitted well below prime-ministerial pay grade (and rarely as exclusive or exciting as we hacks like to imagine). May’s deficiency is a failure to work on professional dialogues with people whose trust she needs. There are few genuine friendships in politics, especially in the international arena. But there are unminuted moments, when the officials are sent out of the room and leaders talk bluntly, peer to peer, about what needs to be done and how the hell to get there. In Whitehall and in Brussels there is a feeling that May is incapable of operating on that level. Worse, there is a suspicion that she doesn’t even recognise the need. If she valued diplomacy, she would never have made Boris Johnson her foreign secretary, nor kept him in the role for so long. The government’s ministerial ambassador-at-large is a stranger to discretion and integrity who routinely undermines his boss’s negotiating positions.

The challenges facing the UK right now would test any leader, and there is a risk of trivialising the difficulty by dwelling on deficiencies in the prime minister’s character.

May has strengths: resilience and dedication. Her survival through electoral humiliation and besiegement by hostile forces in her own party testifies to ferocious will and tactical cunning. But those qualities are good for clinging to power. It is less obvious how they are serving the country. They do not add up to a plan. It is worrying enough to think that May doesn’t know how to get a Brexit deal. The still more frightening thought is that she doesn’t value – or even understand – what it is successful leaders do when they make deals.

• Rafael Behr is a Guardian columnist