The Conservative party has become seriously unserious about government. Trouble piles up at the prime minister’s door with the intensity of a macabre circus: one scandal stumbles into the next, then in comes another, and another, each tripping over the one before; ridiculous without being funny.

Heading the nasty clown parade is Boris Johnson, the foreign secretary. He told a parliamentary committee last week that a British woman imprisoned in Iran was in that country to teach journalists. But Nazanin Zaghari-Ratcliffe’s employer and family insist she was in the country to visit relatives. Tehran says she was agitating against the regime there – an accusation given fresh impetus by Johnson’s remarks. That isn’t a gaffe. It is culpable negligence.

If hope lingers that the foreign secretary has a grip on Middle East policy, let the international development secretary dispel it. Priti Patel flew to Israel over the summer for a “family holiday” that included such commonplace leisure pursuits as meeting the prime minister, Benjamin Netanyahu, and discussing highly controversial uses of the UK’s overseas aid budget. The Foreign Office did not know about the meetings in advance (although Patel at first implied that it did).

The prime minister learned about the meetings only after she had hosted Netanyahu in Downing Street last Thursday. Opening private back-channels to foreign powers is a hefty breach of the ministerial code, as May might recall from 2011, when Liam Fox resigned after a similar offence. At the time of writing, Patel and Johnson were still in post.

Theresa May is trapped in involuntary generosity to a rogue cabinet. She cringes at the thought of reconfiguring her top team, as was made clear last week when Michael Fallon stepped down over allegations of sexual misconduct. To her credit, she took a prompt, stern view of her defence secretary’s alleged record of lunging indecency and steered him out. But her choice of Gavin Williamson as the replacement turned an assertion of authority into a symptom of incapacitation. Williamson was her chief whip and Downing Street confidant. His promotion was not a reflection of his credentials but a desperate fix, born of panicky desire to make problems just go away.

Tory MPs’ nostrils never miss the scent of weak leadership. Within minutes of Williamson’s appointment, the new defence secretary was the subject of a ferocious, expletive-laden whispering campaign. Colleagues said he was a self-serving, unqualified opportunist. That is a standard line for jealous rivals, of course. What made hostile eruption significant in this case is that much of it was proxy criticism of May. It expressed contempt for a prime minister unable to see further than one move ahead, filling a hole with the closest peg at hand, and probably manipulated into doing so by the peg itself.

Williamson’s departmental duties will keep him away from May’s tiny circle of trusted advisers. He was one of “the two Gavins”, the other one being Barwell, former MP for Croydon Central, now the prime minister’s chief of staff. Their duumvirate was credited with bringing some order to a No 10 operation that collapsed when May lost her parliamentary majority in June.

The Georgian houses still stand but, beyond that, it is hard to know what ‘Downing Street' means or wants any more

The other key player is Damian Green, the first secretary of state and an old university friend of May; now himself the subject of a cabinet office investigation into allegations of inappropriate sexual advances towards a young Tory journalist, and of storing pornography on an office computer. He firmly denies wrongdoing but his utility as May’s consigliere, meanwhile, is compromised.

Journalistic convention uses “Downing Street” to describe a power base that holds opinions, makes decisions, imposes the prime ministerial writ. That rhetorical device is now misleading. The Georgian houses still stand but, beyond that, it is hard to know what “Downing Street” means or wants any more. The election did not just rob May of a mandate. It shook her confidence, fractured her will and clouded her horizon. She battles on from a profound sense of public duty, but the impression across Whitehall and in Brussels is that she can manoeuvre only in tactical pigeon-steps. She has reached that morbid state of rolling crisis where success is defined as making it through the day.

There is no government “machine” worthy of the name, and on many issues no government line to defend. In two weeks, the chancellor will deliver a budget of punishing fiscal constraint, while public patience with austerity is spent. Philip Hammond has made enemies enough on his own side for daring to see Brexit through the lens of financial stability, not Eurosceptic theology. He is certain to be attacked by one Tory faction or another. Can he count on the prime minister’s support? Would it even help?

May looks overawed by her problems. The next phase of Brexit talks can be unlocked by a one-line concession on commitments owing to the EU budget. But for that, the prime minister must have a story to tell the public about what they get for their money. She doesn’t know. And she can’t sell compromise to a party geed up by hardline MPs to believe that the collapse of talks would be no bad thing. They only keep her in office because they believe her weakness makes her pliable to their revolutionary demands.

May was a convert to Brexit last year because she had no choice, and because she saw the referendum result as the manifestation of deeper public discontent. Yet much of that anger was tangentially related to EU membership, and will be exacerbated by the costs of leaving. Her recent party conference speech made headlines for its choked delivery, but the now forgotten text was revealing in its assertion of vague priorities separate to the task of steering the UK out of its European dock.

May’s most stubborn delusion is the idea that she might be remembered for some vague, undeveloped social justice agenda, with Brexit painted as the background. So Britain has a prime minister who is propped up in office to do just one thing, which happens to be the one thing she is least intellectually and practically capable of doing.

It is tempting to write that things cannot go on like this, but they can – for a while at least. If proof that May could not govern were sufficient to make her give up, she would have stopped by now. Some other drive sends her ever onward towards her gruesome political martyrdom. That force, undoubtedly formidable, is not serving the country of which she is only nominally a leader.

• Rafael Behr is a Guardian columnist