This was compelling political theatre. On Wednesday Theresa May sent the country a message about authority. Summoning the cabinet to Chequers and then summoning the television cameras to record her opening statement, she was saying unmistakably: “Keep calm and remember who’s boss.”

But the pith of her short message – no covert attempt to stay inside the EU, no second referendum – made clear which side she is coming down on, despite No 10’s “motherhood and apple pie” briefing that Britain’s future relationship with Europe will involve controls on immigration and be good for trade. The simple truth is that much as we may want access to the single market with no free movement of labour, that is not, and never will be, on offer. By promising to push ahead so firmly with no second referendum and no early general election, May has given comfort to the hardline cabinet Brexiteers.

We know now that her first priority is Conservative unity, even above an easy election victory. Some Tory commentators and politicians are horrified that she has not chosen to go to the country early. Labour, they say, is in a worse state to fight an election than for 35 years, riven from top to bottom. This is the moment to strike, they plead. You shouldn’t waste chances like this.

But May is a cool customer, and she has decided to play long. I assume that during her Alpine walking holiday she concluded that she has nothing to fear from other parties and everything to fear from her own.

If, as the polls strongly suggest, Jeremy Corbyn wins the Labour leadership again, there will be moves in the parliamentary Labour party for a breakaway, plunging constituency parties into the turmoil of loyalty oaths and feuds. If (unlikely, I know) it’s Owen Smith, the base and the leadership will be at war. Either way, it doesn’t seem likely that the official opposition will grow more appealing or stronger in the next few years. Let them stew and twist, seems to be May’s approach.

This has profoundly disturbing implications. We have a one-party hegemony. The prime minister, looking around for sources of serious political pushback, knows they are inside her party. The momentum isn’t coming from Momentum: it’s all from the right.

And they are riding high on recent good economic news, which helps the narrative that Brexit was a triumph of popular common sense. However, consumer confidence and employment figures mean nothing yet.

Until new tariffs start to bite, until major City players unable to get their “passporting” deals to continue trading inside the EU start to leave London, until there are concrete examples of major investment being withheld, we can’t begin to assess what leaving the EU actually means for our long-term prosperity. Declaring Brexit a triumph now is like punching the air with delight because you’ve beaten the field in the first 100 yards of a 10-mile race.

Does May understand this? Maybe she does. And perhaps what she’s doing is carefully giving rope to the hard right, so they can hang themselves. Plenty of time – no election yet, no “backdoor” EU membership – let’s see what Boris Johnson, David Davis and Liam Fox actually come back with from their negotiations. If it’s grim for business and prosperity by the time of a 2020 general election, the right will be discredited.

However, there is a darker possibility, which is that May isn’t playing a tactical game; that she has accepted their agenda. In normal political times the not insignificant number of Tory MPs who don’t like Brexit would be able to argue for delay, for another chance for the electorate to have their say, pointing out that getting the terms of Brexit wrong would be a gift to Labour.

But at the moment, with opinion polling suggesting a future Tory majority of well over 100 seats, there is no political pressure at all. Labour’s rhetoric about “taking the fight to the Tories” seems merely forlorn.

The Tories are waiting and watching for a Jeremy Corbyn victory followed by the deselections of “Blairites” and moderates. Labour’s battles will be vicious and local, and will leave lasting scars across the political landscape. There is no chance that it will all be healed, forgotten and forgiven by 2020.

But if the Labour centre-right decides to break away and form a new party then the Tories are in an even better position. Across most constituencies, the anti-Tory vote would be divided at least three ways – Corbynite Labour, the new party and the Liberal Democrats – perhaps with the Greens challenging too. Under our first-past-the-post system, with the Tories facing such a divided opposition the result would be slaughter.

And then, as the Guardian revealed at the weekend, there is the potentially devastating effect of the boundary changes, which can’t really be brought in before an early election but will radically tilt the field by 2020. We are, in short, lacking the usual checks and balances that parliamentary politics normally provides. We are going into the huge Brexit experiment with the tiller of state tied fast in a single position, without proper parliamentary opposition and under a new leader who has only to look in one direction to maintain her position.

That’s what May’s political theatre on Wednesday implied. Perhaps she was playing a cynical political game – but I fear she wasn’t.