The Leavers have had a tough two weeks. First Johnson, then Gove, and finally Leadsom, all vanquished – no wonder David Cameron was whistling. The next occupant of Number 10 will be from the same side of the Conservative Party as him. George Osborne will either stay as Chancellor or be replaced by another advocate of Remain. The grim faces of Leadsom's supporters on Monday morning told the story: they were outdone.

But there is more to come from Leave. The facts of political life under Brexit still favour them. For a start, Prime Minister Theresa May will rely on Leavers for a parliamentary majority. Then, as Government business resumes under a new ministerial team inevitably featuring many Leavers, the day-to-day reality of still being bound by EU law will create controversy.

It might be the proposal for state aid to stop a factory from closing, a new judgement from a European Court, the burdens on business of a new directive, or something entirely bananas – all the ways in which Leavers have styled outrage in the past over Europe are still available to them now.

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The new PM will say, of course, that it's only a matter of time until we’re on our way out. Yet if she wants to keep open the option of joining the European Economic Area then European laws will not be shed so easily. We won't be free with one bound, the Leavers will discover, and then the question is whether they will stay quiet out of loyalty or speak to voters about this perceived treachery.

Already some Leavers, including Bernard Jenkin, a Select Committee chair and one of the pallbearers at Leadsom's withdrawal, are arguing that we should repeal the European Communities Act in a unilateral declaration of independence. Forget the invocation of Article 50, let's take back control right now. Oliver Letwin – put in charge by David Cameron of preparing the options for the new PM when a long leadership contest was envisaged – hasn't helped May by saying that such ideas are worth considering.

Now she will have to talk down those who are in a hurry to leave. It's easy to imagine some Leavers, if they end up as ministers, trying to break free and yet being compelled by May to stick with what EU law requires their departments to do.

The negotiation with the EU on our withdrawal will provide other flash points. There might be two kinds. The first will arise from the typical cross-Whitehall haggling where ministers will try to push their asks up the Government's list of priorities for the negotiation. If they get knocked down and have to front that failure, this will store up resentment. It would be a smart move by the new Prime Minister to put a Leaver in charge of holding this ring. But then the second kind of trouble will arise when we don't get our way with the EU.

We are accustomed to having a veto in Europe, which we use when it really matters. We won't have a veto over the exit deal – not once we've triggered Article 50 – and the clock is ticking. If we don't agree to what we're offered, then we leave without a deal.

We will have some negotiating counters of our own – the EU citizens living in the UK, for example, to whom May has refused to make any promises – but Leavers may advocate a tough line on issues such as this and May could find that she has little choice but to take it.

Brexit protest: Thousands march in London Show all 12 1 /12 Brexit protest: Thousands march in London Brexit protest: Thousands march in London A woman poses with a home-made European Union flag as Remain supporters gather on Park Lane in London to show their support for the EU in the wake of Brexit PA Brexit protest: Thousands march in London Remain supporters demonstrate in Parliament Square PA Brexit protest: Thousands march in London Tens of thousands of people gathered to protest the result of the EU referendum PA Brexit protest: Thousands march in London A majority of people in the capital voted to remain in the European Union Reuters Brexit protest: Thousands march in London Protesters chanted: “What do we want to do? Stay in the EU” PA Brexit protest: Thousands march in London The march follows a similar rally in Trafalgar Square that was cancelled due to heavy rain – but which tens of thousands of people turned up to anyway Reuters Brexit protest: Thousands march in London Britain voted to leave the European Union in a referendum by 52 per cent to 48 per cent Reuters Brexit protest: Thousands march in London But support for the Leave campaign in urban areas and among young people was significantly lower Rex features Brexit protest: Thousands march in London Marchers gathered at Park Lane at 11am and marched towards Parliament Square PA Brexit protest: Thousands march in London Some protesters held up baguettes in a display of affection for our continental neighbours PA Brexit protest: Thousands march in London The disparity between different parts of the country has promoted a four million signature petition calling for a second referendum and even a renewed push for Scotland to cede from the UK PA Brexit protest: Thousands march in London The event’s organiser, King’s College graduate Kieran MacDermott, wrote: “We can prevent Brexit by refusing to accept the referendum as the final say and take our finger off the self-destruct button" Reuters

There will be many tense encounters in the Commons when she returns from summits and is pressed on whether she is being as hard on Europe as they want her to be. The privilege the Leavers will enjoy is that they never had to describe their manifesto for the negotiation; they can criticise from a fresh start.

This isn’t just a question of defining the next blood feud in the Tory party. It really matters. A 'hard Brexit', involving less access to the single market, tighter immigration, could result in lower growth, less money for public services and a tougher, meaner politics – and a tougher and meaner country, too.

It may be that Prime Minister May is the match of all these challenges. She won the leadership battle with remarkable poise. But we might soon reflect that, in the end, it was the Leave campaign that won the war.