It is now a month since Britain voted to leave the EU. By common consent, at home and abroad, it was a massive historical moment. The best of times for some. The worst of times for others. Some compared it to the fall of the Berlin Wall. Others to the defeat of Hitler. Yet with the exception of the banner-wavers who occasionally turn up chanting “Theresa May/Don’t delay” and calling on the prime minister to trigger article 50 of the Lisbon treaty, the passions of June have dissolved in the torpor of July. Four million people signed a petition to hold a second referendum after the 23 June result, but little of their indignant spirit remains a month later. There have been few material economic consequences of the Brexit vote yet, especially in everyday life.

True, there have been a very large number of other convulsive events in the past month to distract attention. The Turkish coup attempt, the Bastille Day tragedy in Nice, a new prime minister, a Labour leadership contest, Chilcot, Trump. Yet the national shrug of the shoulders about the Brexit vote, one month on, is both striking and disconcerting. The ConservativeHome columnist Paul Goodman this week compared the mood of post-Brexit reconciliation in Britain with the successful restoration of the Stuart monarchy in 1660. It’s not a very accurate historical parallel, but one can understand what he is getting at.

‘With the exception of the banner-wavers who occasionally turn up chanting “Theresa May/Don’t delay” and calling on the prime minister to trigger article 50 of the Lisbon treaty, the passions of June have dissolved in the torpor of July.’

May has had a month she could not have dreamed of. If the vote had gone the other way she was the big candidate for the chop in David Cameron’s victory reshuffle. Instead she is his unchallenged successor, destroying the liberal metropolitan Tory project in 24 hours, and enjoying a triumphant debut at prime minister’s questions against a second-rate Jeremy Corbyn. In her early dealing with the leaders of Scotland, Wales, Germany and France, she has not yet put a foot wrong.

All the same, Brexit overshadows everything in the May premiership. She is not in denial about it; nor should anyone else be. Brexit is still by far the most important change in our politics for decades, just as it was when the result was declared. It will dominate British government for years. Its consequences will be profound. Do not be distracted. The Tories’ handling of Brexit matters far more than the flounderings of the Labour party.

May’s visits to Germany and France this week were assured performances. But it is far from clear, including probably to her, what exactly she wants. May repeatedly intones the mantra that “Brexit means Brexit”. But what does Brexit actually mean? She does not say. A week into her premiership we are none the wiser.

What it does not mean is what remainers would like it to mean. Those who want a minimalist Brexit want the UK to enjoy a post-Brexit relationship with the EU along Norwegian lines, with full or almost full access to the EU single market. That’s what UK industry, and many unions, would like. It’s what the City of London would like too. But the problems with that sort of relationship are that it means accepting freedom of movement and agreeing to make a contribution to the EU budget. That is fine for liberals. But it is unacceptable to post-liberals like May.

Politically, free movement is anyway an impossible sell now. May commands the scene but she only has a Commons majority of 16. Anti-European Tory backbenchers put down clear warning markers about both market access payments and migration controls in PMQs this week. Even if she wanted a Norway deal, May knows enough about recent Tory history to know that her MPs can make her life impossible if they choose.

She must also sense that free movement could be catastrophic electorally for the Conservatives. Freedom of movement would be too high a price to pay to maintain the newfound but still fragile post-Cameron unity in the party. But there has been a post-referendum shift in Labour thinking, especially among pro-Europeans, towards tighter controls. An unlikely prospect though it is, May does not want to be faced by a believable Labour party that casts her Brexit deal as soft on free movement.

‘François Hollande will have said no too [to a deal which combined access to the single market with controls of freedom of movement]. He cannot afford to set a precedent that Marine Le Pen would demand to emulate.’ Photograph: Boris Horvat/AFP/Getty Images

The most important reason why this is unlikely is that May herself is a long-term supporter of tighter controls. She is not going to change that now. Perhaps she asked Angela Merkel this week if the UK could get a deal which combined access to the single market with controls on freedom of movement from the EU. If she did, Merkel will have said no, because such a concession would subvert the single market ethos and rules. François Hollande will have said no too. He cannot afford to set a precedent that Marine Le Pen would demand to emulate.

What this means for British politics has still not been sufficiently appreciated. The May government ultimately faces a choice between trying for a Brexit that the City and the financial sector wants, and trying for a Brexit the Brexit voters want. It is a choice May cannot avoid. Yet everything May has said about domestic priorities since entering the leadership contest suggests that she intends to deliver for the latter, the Brexit voters, rather than for the former, the City.

Naturally, May will try to please both constituencies as much as she can. So the eventual Brexit package will not embody as stark a choice as I have implied. There will be exceptions to permit certain types of migrant – the devil is in the detail there. And there will be as many safeguards for the City as the government can achieve. Nevertheless, in a few months’ time, she has to switch the treadmill on. Once she triggers article 50, she has got to know where she intends this journey to end.

That is why the great story of the May premiership is her attitude to the City of London. The balance between the financial sector’s interests and those of anti-immigrant, left-behind Britain will be the acid test for her government. It will test the bond between the communitarian May and her more liberal chancellor of the exchequer, Philip Hammond, to the full. And it will test the credibility of the remarkable words May delivered in her Birmingham speech on 11 July, and repeated on the threshold of 10 Downing Street a week ago.

In the end, everything she has said points to Theresa May preferring a Brexit that delivers tighter border controls to a Brexit that delivers the market freedom the banks want. Is she ready for that choice and all that could follow it? The implications for Britain and its new prime minister would indeed be historic.