Only a small minority of the people who support a party become members. An even smaller number then turn into members who don’t actually support their party. Logically, there should be none, yet I meet them these days with surprising frequency.

Some are liberal-minded Tories who feel that Brexit has tilted their party’s centre of gravity towards intolerant nationalism. But their distress pales beside the anguish of Labour people who cannot stomach Jeremy Corbyn’s control of the party.

Jeremy Corbyn accused of being 'figurehead for anti​​semitism' Read more

Tory rebels are unhappy with Theresa May, but can envisage worse: their nightmare is a leader – Jacob Rees-Mogg, perhaps – whose beliefs would make them want to tear the rosette from their lapels. That nightmare is the day job for some Labour MPs.

There is nothing new about friction between the pro-Corbyn movement and its malcontents. The dissenters tried to unseat their leader once and failed. Their confidence that contact with the sharp end of an election would burst Corbyn’s bubble then proved misplaced. And so, after last June, Labour’s demoralised and disoriented dissidents burrowed into the soft mulch of tribal loyalty and hibernated.

Yet in the past few weeks they have been stirred awake. The cause is a sequence of positions Corbyn has taken – or failed to take – in three areas: Russia, Brexit and antisemitism.

There is already an anti-Brexit party – the Lib Dems – who look like a tired nostalgic tribute band

When May blamed the Kremlin for the attempted murder of a former spy in Salisbury, the Labour leader invited her to reconsider. He suggested that Russian authorities be asked to verify the provenance of a nerve agent known only to have been developed in Russian laboratories. Here was the opposition leader apparently straining to exonerate a regime plausibly charged with a chemical weapon attack on British soil.

Meanwhile, Corbyn has firmed up his credentials as a Brexit true believer. In a speech in Dundee this month, the Labour leader made it clear that his reasons for wanting to break away from the EU single market were every bit as ideological as those of his Tory leaver counterparts – symmetrically positioned as far to the left as they stand on the right. When, last week, Owen Smith, shadow Northern Ireland secretary, backed the idea of a public vote on Brexit terms, he was fired from the front bench.

Facebook Twitter Pinterest ‘Tory rebels’ nightmare is a leader – Jacob Rees-Mogg, perhaps – whose beliefs would make them want to tear the rosette from their lapels.’ Photograph: Toby Melville/Reuters

That news broke on the day that a row erupted over a Facebook comment posted by Corbyn in 2012, expressing support for an artist whose mural was due to be erased from a wall in east London. The work showed caricatured Jews playing Monopoly on the backs of emaciated bodies. Corbyn’s encouraging comment began with the word “why?” The answer should have been obvious. And just a brief interrogation might have exposed the artist’s own explanation: “Some of the older white Jewish folk in the local community had an issue with me portraying their beloved #Rothschild or #Warburg etc as the demons they are.”

It was hardly the first time Corbyn had come face-to-face with blatant antisemitism and somehow failed to see it. When offending items are brought to his attention, he regrets that offence was caused. But he also has a history of casual solidarity with the offenders. He condemns “pockets of antisemitism” in Labour but he can’t acknowledge that those pockets are sewn into his movement. The darker recesses of anti-capitalism, where “Zionist” cabals are believed to be the epicentre of evil, are fringes to a banner that is embroidered with Corbyn’s name.

While no item in the Russia-Brexit-antisemitism sequence surprises Corbyn’s critics, the unfolded triptych should be revelatory to those MPs who were numbly traipsing along in his shadow, hoping that something might turn up. It won’t. He is their leader. If they stand for election, they should want him to be prime minister. If they believe, as many on the left do, that any Labour government is unquestionably better than any other kind, they must be honest about the price of that choice. If they think vital skills in a prime minister include recognising antisemitism at first sight, trusting UK security services over Vladimir Putin, and fearing that a hard Brexit is bad for Britain, they might be in the wrong party.

Inevitably there is chatter about alternatives. Imaginary parties crop up wherever beaten Blairites rub shoulders with disconsolate Cameroon Tories. And the conversation always stumbles against the same obstacles: no leader; no clarity about what the “centre ground” means, beyond an assertion that May and Corbyn have abandoned it. Dislike of Brexit is a common grudge, but not a long-term programme. It is a sentiment that covers a wide spectrum of political opinion in parliament and beyond – Welsh and Scottish nationalists, fiscal conservatives and anti-austerity social democrats.

Facebook Twitter Pinterest ‘The Russia-Brexit-antisemitism sequence should be revelatory to those MPs who were numbly traipsing along in his shadow.’ Photograph: Owen Humphreys/PA

Contempt for the way May has handled the Brexit negotiations is a sentiment that might animate George Osborne in his chair as editor of the Evening Standard, and Caroline Lucas, the Green MP for Brighton. That doesn’t mean they are natural allies in a putative coalition of remain-spirited, metropolitan social liberals. Besides, there is already an anti-Brexit party – the Lib Dems – who look like a tired nostalgic tribute band to an era of politics that isn’t coming back.

The 37th anniversary of the founding of the Social Democratic party went unmarked yesterday, because the SDP’s main legacy is as a cautionary tale to schismatic Labour MPs. It might be very hard to convert a Corbynised party into something else, but that doesn’t mean it would be any easier starting again from scratch.

Meanwhile, Brexit-sceptic Tories are exercised by different calculations. First, their horror at the idea of Corbyn in Downing Street easily matches their dislike of Brexit, so they flinch at any course of action that might precipitate an election. And second, while they don’t like May’s habit of yielding to pressure from dogmatic anti-EU backbenchers, they also recognise that, as long as she is in office, the fanatics do not control the whole government. While Labour’s moderate faction is already in psychological exile, its Tory counterparts still feel some kind of political investment in their current leader.

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But the biggest challenge, for both Labour and Tory dissidents, is knowing what the alternative vehicle they crave even looks like. This is a catch-22 problem: there is no platform without leaders willing to stand on it, and none step forward without a platform to hold them up.

Meanwhile, there is a certain comfort in sticking within existing tribal reservations, doing doctrinal battle with internal enemies. There is a sense of righteous solidarity, being part of a heroic resistance. But that feeling is also a trap. Internal party warriors are good at knowing what they are fighting against. But in politics that is the easy bit. The hard part is telling the rest of the country what it is you are fighting for.

• Rafael Behr is a Guardian columnist