Let’s start with the headlines. We are going to get a different kind of Brexit, but we will leave. The Conservative hard right is now both isolated and dangerous. And although Labour failed to win the election, Jeremy Corbyn’s party has already had a big influence on the new government. Oh, yes, and Theresa May stays . . .

Those are immediate conclusions based on simple political logic. Yet we are not living in a period suited to confident predictions. Parliaments with such tiny majorities are at the mercy of random events, from heart attacks to obscure rows over completely unpredicted issues. As I write, the Tories haven’t even concluded successful negotiations with the Democratic Unionist Party (DUP), and the Queen’s Speech may have to be postponed while May continues her impressive speed-running buffet, scoffing industrial quantities of humble pie.

In such a strange political landscape, the safest thing is to step back a few paces and begin with what we know for sure. First, the Conservative Party is still, just, in control of the country. Its authority is badly weakened and its grip is flimsy, but with the DUP it has the numbers to win the Westminster votes – which, in our system of extremist parliamentarianism, is almost all that matters.

Second: in that case, what now matters most to the Tories? They are, more than ever, a mixed bag. But there are two things most of them agree on – that to go up against Jeremy Corbyn in another general election any time soon would be an act of suicidal stupidity; and that, one way or another, they would quite like to deliver Brexit.

These banal observations imply that May will carry on as Prime Minister for months and possibly even for several years. A Tory leadership contest now – after all the party has said about the Article 50 clock ticking, and having lost two months already with a catastrophic (for Conservatives) general election – would be so grotesquely self-indulgent that the party wouldn’t recover. Whichever poor sod won the leadership would be under massive pressure to hold yet another election in which, you now have to assume, Jeremy Corbyn’s Labour Party would triumph.

Boris Johnson, rampaging around in the undergrowth and breathing heavily, is, many of his colleagues think, constitutionally incapable of not plotting his next move to the top job. Yet I’ve talked in recent days to several senior Tories from different parts of the party who swear that, in one way or another, Boris will be stopped. Were there to be an election, Johnson would be a formidable hooverer-up of votes, perhaps the only Tory today who could match Corbyn’s charisma. Almost nobody wants Theresa May to lead the Light Brigade into another election. So there may be a time when “call for Boris” actually happens. But that’s for another year. Meanwhile, I have to ask: is the current Conservative position of keeping Johnson as their possible electoral saviour in due course, while at the same time ridiculing and diminishing him at every opportunity, completely wise?

Granted, there are other potential prime ministers around. Vigorously (and quite convincingly) denying that he wants the job, David Davis, robust at 68, is nevertheless the obvious successor to May. He is just about the only minister who understands the Brexit negotiations. He is enough of a right-wing toughie to persuade most of the Tory right of his Eurosceptic bona fides, while also being enough of an economic realist to do the deals necessary on immigration and the legal status of EU nationals.

His job is hugely complicated by the outcome of the election. Because of the mathematics of the new parliament – from Ruth Davidson’s group of Scottish Tories to the DUP and the residual Tory Remainers from England – the Brexit position has to change. May has already admitted as much to the 1922 Committee. Davidson is openly demanding talks with other parties. Labour, also committed to leaving the EU, is being lined up as a potential support for the Prime Minister against “no deal is better than a bad deal” Tory ultras.

Thus a great, glittering bubble of optimism has appeared around unreconciled Remainers. The possibility of a non-Brexit has been whipped into a lather by the interventions of former Tory leaders – Hague, Cameron, Major; by “the door is still open” comments from Emmanuel Macron in Paris and Wolfgang Schäuble in Berlin; and by a fresh initiative from the UK Treasury. But we have to remember that this still depends on the Tory party in parliament and what it thinks its own best interests are. Maybe, just maybe, this thing won’t have to happen, after all: let’s call the whole thing off. Michael Heseltine suggests that Macron, fresh from his victory in France, might team up with Chancellor Merkel to offer the British a deal on immigration sufficient to allow the UK to

stay inside the EU. In short: game on again.

***

The chances of a major British rethink about whether and, if so, how we leave the EU seemed to be boosted by the survival of Philip Hammond as Chancellor. May had planned to sack him (and, I’m told, Boris Johnson, too) if she won a big majority. But Hammond, speaking for a very nervous City, and Johnson, with his more liberal views on immigration, remain firmly in place. According to the Remainers’ bible, the Financial Times, British business leaders, who would rather stay inside both the single market and the customs union, now feel emboldened to speak out. They are dancing round the maypoles in besieged Remainer citadels from Cambridge to Primrose Hill.

So let me teeter forward, clutching a very large bucket of cold water. Remaining in the single market requires – unless there is a very large change of heart at Brussels – relinquishing the idea of controlling immigration. For most who voted Leave, that is betrayal. Tory right-wing Brexiteers would be enraged. John McDonnell, one of the clearest Labour voices on this, is utterly against such a move. If it went forward, I don’t see how half the cabinet could stay in their jobs.

So far, the wounded Prime Minister has tried to lean in both directions with her new cabinet appointments – the dripping-wet Europhile Damian Green on one side and the arch-Brexit merchant and Thatcherite Michael Gove on the other. But it’s a wobbly house of cards. Almost certainly, if she suddenly decided to stay in the single market, her government would collapse. Chaps, comrades, citizens of the People’s Republic of Primrose Hill, it’s unlikely to happen.

What about those interesting numbers in the House of Commons? The Scottish Tory MPs are still members of the Conservative family and Ruth Davidson must be aware of the risk of overplaying her hand. After their good results north of the border, they might be more willing to break ranks and provoke another election; but their English colleagues would (perhaps literally) strangle them. In a minority government, the pull of tribal discipline is unusually strong. The DUP, meanwhile, can be bought off and is philosophically in favour of leaving the EU anyway. And then there are Labour MPs who are against staying in the single market. The more I look at this, the more I feel that, despite everything, May has the numbers for a subtly modified Brexit.

These changes matter. In terms of tone, we will have to stop treating the rest of the EU as opponents, rather than our friends and allies. Meanwhile, we are already seeing the ditching of the “tens of thousands” immigration policy. And that’s probably just the beginning.

This is a shift, not an overhaul: despite some of the rhetoric, ministers were not planning the most brutal of Brexits. They have no intention of slamming the door on talented and hard-working European migrants, nor of having an unnecessary bust-up about the rights of EU citizens living here already. They know full well that some kind of financial price is going to be paid as part of our exit.

The much-debated “no deal” option is a proposal for failure and catastrophic failure only – a negotiating gimmick, not any kind of serious plan. Indeed, I’m pretty sure that the real reason the election was called in the first place was that the Prime Minister realised that the European chief negotiator, Michel Barnier, would require her to make unpopular compromises that she couldn’t have got through the old Commons. Now she will have to get them through in even harder circumstances.

I wouldn’t be surprised if we opted to stay inside the customs union for quite a long time as a transitional agreement; and I would be amazed if even looser and more generous migration deals were not being considered for side agreements. May and her cabinet, however, remain tied to a deal that involves leaving the single market, leaving the jurisdiction of the European Court, regaining full control of British borders and ending large regular payments to Brussels.

Even Philip Hammond and Damian Green, the pro-Europe Tory moderate now installed as First Secretary of State (in effect, deputy prime minister), broadly accept this. I see no sign of that changing. What about the Heseltine suggestion of a new migration deal sufficient to allow the UK to stay inside the EU? A senior minister close to the action retorts briskly: “Too late.”

I suspect that many New Statesman readers will regard the above as the vapourings of a Brexit appeaser. Surely the humiliation of the Prime Minister, who called the general election on the issues of Brexit and her authority, must result in a change of direction – and a big one to boot?

But May, who we have already established is likely to survive in No 10, doesn’t want her political career to end on the disaster of the June 2017 election. She wants to do what she has said she wanted to do since becoming Prime Minister, which is to deliver what she calls “a good Brexit”. So long as she is there, with this cabinet and with this Conservative Party, the ship of state – leaking and battered – sails slowly but steadily in the same direction. Is that horizon line a watery cliff marking the end of the world, or is it the New World? Nobody knows, but forward we go. Only another election could change this.

In these circumstances, what role does Labour play? The government makes much of the reality that there is no huge difference between what May and Davis say about the Brexit deal and what Corbyn and Keir Starmer say. That’s true – Labour is as committed to leaving the EU as the Tories are. Labour also accepts that it isn’t possible to remain a full member of the single market while taking back control of immigration; and Corbyn’s party, holding so many seats with pro-Brexit majorities, has no wish to appear to be trying to overturn the referendum result.

That said, there are significant differences. Most important, Labour has not committed itself to getting immigration down to “tens of thousands” and would accept deeper judicial oversight on the rules in order to get better access to the single market.

Senior Labour people I talk to are sceptical about an alliance or commission on the Brexit talks of the kind that Yvette Cooper has suggested. Brexit, they point out, sprawls across so much of the political landscape that this would amount to a grand, Continental-style agreement on the future of Britain on everything from workers’ rights to farming and industrial policy: how could Mayite Tories and Corbynite socialists agree so widely?

And yet the Labour Party’s influence is greater than at any time since Gordon Brown went into the fatal election of 2010. I don’t see how May can get most of the austerity agenda, or grammar schools, or root-and-branch NHS reforms, or fox hunting, or the withdrawal of winter fuel payments through this House of Commons. I’m beginning to wonder whether the Conservatives can even get a majority for a continued freeze on public-sector pay and welfare. Again, stand back a bit and you’ll find that, without winning a parliamentary majority, the Labour Party might get quite a lot of what was in its manifesto anyway. That’s what a hung parliament means.

It will enjoy all of that, but it would be lethal for Labour now to relax. To prepare itself for the next election, it needs to be in the right policy position to win an overall majority. John McDonnell and his team worked hard with outside experts to produce a costed manifesto, but their numbers still depend on optimistic assumptions about economic growth, and there is more to do. “The language of priorities is the religion of socialism,” said Aneurin Bevan in 1949 to an angry party conference in Blackpool during the greatest Labour government. It remains true. If Team Labour flinches from making some hard choices in private now, it will come to regret it when the next election is called.

And, yes, one way or another, the grumpy rebel talent that turned its back on Jeremy Corbyn must be allowed to shuffle back. Corbyn is a forgiving and relaxed man; that is not entirely true of everybody around him. The Tories want more time before the next election but Labour needs to use that time busily, too.

In all this, over the next few years, Brexit will loom over everything. In the cod-medieval corridors of Westminster, in coffee rooms and ministerial offices, in bars and on the paths of St James’s Park, Tory-Labour, Tory-SNP, Tory-Tory (and so on) conversations will now shape our future.

One clear example is judicial oversight. The Prime Minister is determined that Britain will completely free itself from the European Court of Justice. Michel Barnier has been equally clear, in a speech he made in Florence, that EU citizens living in Britain must have their rights protected in the long term by European judicial oversight. David Davis’s response to that, which is that they will have their rights guaranteed by British law under our Supreme Court, tied to an international treaty, may not wash. So there’s a crash coming. (By the way, I would expect a theatrical walkout and angry words quite soon, as the negotiations start. And when that happens, my strong advice is not to take it too seriously. There is going to be a bit of gorilla before everybody settles down.)

***

Going beyond the rights of European citizens, there is the question of how trade disputes will be handled after Britain has left the EU – lawnmower noise levels, the packaging and description of smoked salmon, you name it. The Tories are determined to get us out of the ECJ and if May can’t manage that, her MPs may then move against her. Labour’s view is that there must be an independent court, which companies and individuals can approach, not just governments.

For both trade disputes and individual citizen rights, the obvious solution is a new court structure comprising both ECJ judges and members of Britain’s Supreme Court – call it the “Guernsey Court” option. This won’t please the Tory right or those with the hardline independence view represented outside parliament, still, by Ukip. It is exactly the kind of issue on which the opposition parties might have to come to the government’s aid in the weeks and months ahead. The same may go for agreements on future work quotas and on the appropriate payment for leaving.

If this is right, the obvious conclusion is that Britain is now heading for a softer exit than it was before the election. It will fall far short of retaining membership of the single market, as demanded by unreconciled Remainers. It is possible, particularly because of the DUP, that we may stay in the customs union – but note that, if we do, the Department for International Trade would become almost immediately redundant and we might then see the resignation of Liam Fox. At the least, we will see more compromises over judicial authority and migration and money in return for better market access.

This is probably the best deal now available. Yet even this ignores two huge potential problems. The first is that the rest of the EU, with its own agenda, may not be interested and may want to use the weakness of the May administration to grind British noses in the dust – or, in blunter terms, make us pay more money. Our wild and at times chaotic politics encourages us to see the negotiations as if they were almost one-sided. This is very, very stupid. On the other side, there are plans, and priorities, and worries, and some very big egos. As we leave, they won’t all wish us well.

That takes me to the second big problem. The worse the EU side behaves, the more the popular press and the Tory right will portray this as a nationalistic fight against Continental enemies. Despite the election result, don’t write all those people off yet. There is still a considerable Tory group that would like to see us exiting with no deal at all and that, angry at the compromises being made in our complex new parliament, may yet decide to revolt against May-Green-Davis-Hammond and bring the House down. There is a Götterdämmerung option.

Let’s take another step back. By and large, parties of the centre right get into trouble when they find themselves divorced from the interests of big money and big business. But we now live in a political environment, since the 2008 crash, in which popular revolt against big money is expressed on the right as well as on the left. To some extent, the Tories represent both the problem and the revolt against the problem. That’s part of the reason why May’s simple appeal for leadership and stability failed.

And it makes the May cabinet a buzzing electric switch box of tangled pressures, full of heat and crackle, in which the interests of the City, hi-tech business and universities on one hand and the demands of poorer voters across England on the other are played out day after day. If May, Hammond, Davis and Green manage to pull off an acceptable compromise and deal, it would be a heroic achievement to put against the appalling Conservative election campaign. However, they can’t do it any more without immersing themselves in old-fashioned parliamentary politics and deal-making.

My advice to all newspapers, media groups and websites is to tool up – get out there and hire more political and parliamentary correspondents, right now. This is going to be the most exciting parliament of my lifetime.

The tenth-anniversary revised edition of Andrew Marr's book “A History of Modern Britain” is published by Pan