History has few iron laws. Yet a reading of British history suggests at least one exception. Those who are at first described as mutineers invariably win the argument. Mutinies happen because a system has reached breaking point and cannot continue.

The 15 Conservative MPs whom the Daily Telegraph dubbed “The Brexit mutineers” this week can therefore take comfort. They are winning the Brexit argument. They are right to try to strike the Brexit deadline date from the bill, and right to demand proper legislative power over the final deal. These are preconditions for avoiding a hard Brexit that Britain cannot afford.

This has wider implications. Theresa May’s probable loss not only threatens the Brexit project. It also diminishes her authority more generally. She has occasionally attempted – most famously in her speech on the steps of No 10 in July 2016 – to give her party and voters other, positive reasons to support her. But the content has never matched the phrase-making, a failure symbolised in the letters falling off the backdrop slogan about “Building a country that works for everyone” during her party conference speech.

Next week’s budget is this government’s biggest opportunity to reshape the national political conversation. If there is to be a moment at which the May project can free itself from the Brexit forcefield, this is it. The importance of the opportunity can hardly be overstated, because it is the only UK budget in the next five years that will not in practice be overshadowed by the Brexit timetable.

If May’s Florence speech timetable is broadly correct then next year’s budget, 12 months from now, will come at the same time that some of the starkest realities of the UK’s prospective departure from the EU in March 2019 are clarifying. The budget after that, in autumn 2019, will be the first in the post-Brexit transition period, which is supposed to last two years. The autumn 2020 budget will come on the threshold of the end of that transition, while the 2021 budget will be the first under whatever new trade and business relationship has been negotiated with the EU.

If there is to be a moment at which the May project can free itself from the Brexit forcefield, this is it

Because of Brexit, ministerial resignations and rows over sexual harassment and bullying, this budget has crept up relatively unnoticed. The self-absorbed Bourbonesque mood in the Conservative party is so strong that many MPs look at the budget merely as a test of Philip Hammond’s standing. Michael Gove is apparently auditioning for the role, and was said to be ostentatiously using “lots of long economicky words” at this week’s cabinet pre-budget discussion.

Next Wednesday is politically and economically crucial for the future of the Tory party. It is the one moment in this parliament when May and Hammond will have the stage to themselves to make a large statement about the government’s values and the means it envisages for embodying them.

On leadership, May struggles against Jeremy Corbyn in recent polls. YouGov this month has her with only a narrow 34% to 31% lead over Corbyn as best prime minister, with 35% not sure and with May’s net good/bad job ratings of -24 (with Corbyn on +5). But May and Hammond still have a strong 13-point lead on economic competence over Corbyn and John McDonnell in ICM’s late October poll, rising to 21 points among male voters.

Hammond can say discrete and incremental things next week about issues that matter: industrial strategy, infrastructural investment, universal credit, pay, productivity and public spending. It would be surprising if he says nothing significant about subjects such as social housing, diesel cars and student finance. But the largest challenge facing his party is to find a governmental narrative that is unshackled from the strategy of rigid deficit reduction and public spending cuts on which the coalition embarked in 2010, and which remains its cornerstone seven years on.

The politics of this is hard because supply side economics continues to exert a tyrannical grip on most of the Tory party. Most Conservatives still believe that the state is too large, and should be made smaller. A few, among whom Oliver Letwin and Nick Boles stand out, have said publicly that things have now gone too far. Hammond is said to be flirting with pencilling in some tax rises for later in the parliament.

But the economics is hard too. There is not as much money in the Treasury coffers as Hammond had hoped, partly because Brexit uncertainties are holding back investment decisions. Some of this problem may be finessed by crafty measures such as moving housing associations off the public books, announced today. But not enough of it.

As Conservative Home’s Paul Goodman put it today, Spreadsheet Phil must somehow morph into Storyteller Phil next week. Faced with public disgust about tax avoidance, public weariness towards austerity, and public impatience about public service cuts, Hammond simply cannot afford not even to try. It would be a risk too far for the chancellor to assume that public doubts over the kind of Labour economic plan McDonnell set out today would ensure the Tory advantage.

Yet that is by far the most likely course. The Tory party likes to think of itself as the party that helps ordinary people get on. But the present Tory party wills the end without the means. Brexit embodies that, as does austerity, as does the reluctance to do radical and high-profile things about tax avoidance. The budget is a huge opportunity to do things differently and in ways that are consistent with the better traditions of the Tory party. But it won’t happen. The Tory party is too far gone.