On Monday morning, almost exactly a year to the day since the UK voted to leave the European Union, formal divorce negotiations will begin in Brussels. Yet at no point since the referendum has the British government seemed less prepared and less sure about what Brexit should actually entail. During the general election, Theresa May taunted Jeremy Corbyn, saying he would be “alone and naked” in Brussels if he won because he would have no plan. That comment has backfired spectacularly on her – as has so much else. In some quarters, including sections of the Tory party, there were growing doubts this weekend about whether Brexit – and certainly the “hard” version that Theresa May seemed intent on pursuing – would happen at all.

At 10am David Davis, the secretary of state for exiting the EU, will sit down with the EU’s chief negotiator, Michel Barnier, but the hardline Eurosceptic minister will be in a weaker position than at any time in the 11 months since he took the job. An election that May called to give herself a strong personal mandate for taking the UK out of the single market and customs union, as well as rejecting any future role for the European court of justice, failed to deliver her one.

May hoped that, as well as strengthening her own hand, she would humiliate and split the Labour party by winning a thumping majority. Instead, as Labour’s Brexit spokesman Keir Starmer told the Observer, it is her party that is now in turmoil, yet again, over Europe, and consumed once more by its own divisions. “Brexit had the potential to tear the Labour party apart. But after last week’s result, it looks like the Tories now face that problem,” said Starmer.

For months, Tory Remainers had licked their wounds and resigned themselves to defeat, as May drove “hard Brexit” forward. It genuinely looked like the internal Tory war over Europe could be over. Now the tables have turned, the Remainers are roaring back, and the arguments are more visceral than ever. When they returned to the House of Commons last week, Remainer spirits, as typified by Anna Soubry, were revived. One minister sacked by May last summer, and who is close to David Cameron and George Osborne, said the internal battle that was about to break out between pro-and anti-EU factions could well be terminal for the Conservative party. “We will split. We hate each other,” he said. “We will do whatever we need to do to kill hard Brexit. She does not have a mandate for it.” Another Europhile former minister said the only way forward now was to drop the “utter madness” of Brexit altogether. Writing on Observer.co.uk today, Tory MP Dominic Grieve, a prominent Remainer, says dropping out of the single market altogether and leaving EU security arrangements would do untold damage: “Access to a single market with our European neighbours for our goods and services is and will continue to be the most important foundation for our future prosperity.”

The rhetorical counterblast was equally strong from the Eurosceptic trenches. A convinced hard Brexiter and leading light in the 1922 committee of backbenchers said any backing away from hard Brexit would lead to civil war: “If we drop Brexit or backslide at all, there will be a revolution,” he said, meaning one in both the party and the country.

So weak did May find herself in the seething post-election Tory party atmosphere that she had no option but to plump for a defensive reshuffle during which she promoted leading figures from both sides of the argument in the desperate but probably forlorn hope that they would neutralise one another. Damian Green, the pro-EU cabinet minister, was elevated to the role of deputy prime minister while Michael Gove, co-leader of the Leave campaign, returned to the cabinet as environment secretary. Philip Hammond, the chancellor whom she had intended to fire because he was so pro-single market, was kept on despite demanding a more business-friendly approach to Brexit as a condition for staying. The strongly pro-EU and vocal Alistair Burt was whipped back into the Foreign Office where he had been before, while Steve Baker of the ultra-hardline anti-EU faction was made a minister in Davis’s department. “Can you imagine the inter-departmental conversation between them?” asked one moderate Tory MP.

May’s attempt to bind opposites together will soon be put to the test. The biggest problem she faces will come in parliament when she tries to steer the many Brexit bills she needs to pass on to the statute book. They will cover issues as fundamental as trade, immigration and the rights of EU citizens. All eyes will be on Wednesday’s Queen’s speech, to see which ones she dares to include alongside the great repeal bill, which will transpose EU law into UK law. Without a Commons majority, and reliant on the 10 DUP MPs (who will veto any deal that involves a hard border between the north and south of their island) it will only take a handful of Tories to rebel and she would be defeated – and possibly forced to call a confidence motion, as John Major was during the passage of the Maastricht treaty. The broadly pro-EU House of Lords lies ready in waiting too, knowing it can now cause trouble because hard Brexit has no election mandate.

Facebook Twitter Pinterest Steve Baker, a hardline anti-EU Tory, has been appointed a minister in David Davis’s department. Photograph: Peter Nicholls/Reuters

In its leader article on Thursday, Osborne’s Evening Standard gleefully anticipated the parliamentary impossibility of May’s task and that of her whips. “It must also be dawning on the government’s business managers that outside the customs union any trade deal will need to be passed through the House of Commons – good luck assembling a majority for allowing imports of Chinese steel and American hormone-injected beef, let alone foreign companies bidding for public-sector contracts.”

How far Labour is prepared to go in finessing its own Brexit policy towards backing a softer version – one that at least entertains the idea that full membership of the single market should be kept on the table, conditional on a deal to change freedom of movement rules – will be crucial in the coming weeks. If Labour shifts this way it will be on the same page as many Tory Remainers. Starmer appears to be edging in that direction and has called for a “new approach” from the government with “a stronger emphasis on retaining the benefits of the single market and the customs union”. But Corbyn and shadow chancellor John McDonnell have thus far insisted that the UK has to leave the single market, while pushing for maximum access, on the grounds that the British people voted in the referendum to restore full control over immigration. For them, it will probably come down to what delivers the best chance of bringing down the government and triggering another election.

Labour is keen to exploit the government’s deep discomfort. May insists that she will press ahead with the same hard Brexit policy that she announced in her white paper and letter to the European council triggering negotiations – but for which she failed to win a parliamentary majority. “It really is extraordinary,” said Starmer. “We’re entering the most important negotiations Britain has faced for generations and we’re doing so in the worst possible position. It’s a real mess. And as Theresa May said herself, it’s a mess of her own making.”