Theresa May’s Grimsby speech offered no new plan to break the Brexit gridlock. This week is crunch time for her deal and the speech only confirmed the need for parliament to chart a way through.

For months she has hammered home the message that passing her deal is “in the national interest”. But amid the endless analysis of textual shenanigans and parliamentary hullabaloo we have completely lost sight of what that means. If the deal passes this week it will soon become clear to all sides of the debate that it is the very opposite.

Conservative MP for West Dorset Oliver Letwin captured the mood of the nation on the withdrawal bill’s last pass of the Commons. “I’m past caring what the deal is we have,” he said. And who can blame him? After three years of cakeism, and presented with the real trade-offs, no-dealers see the national interest as represented by regaining some lost pure sovereignty, whatever the cost to our prosperity, social cohesion and standing in the world. Meanwhile, a growing majority tell pollsters that they now think Brexit was a mistake.

Many Remainers think revoking Article 50 is in the national interest because it would stop the damage to the UK’s reputation and revive the economy, despite the undeniable force of the June 2016 mandate.

Amid such polarisation, pragmatists are inevitably tempted to take Letwin’s view that it is in the national interest to sign up to May’s deal whatever she comes back with. It would, after all, discharge the referendum mandate while securing the economic lifeline of a steady-state transition period. This is profoundly mistaken.

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All sides, particularly many pragmatists, misconstrue what’s in the national interest. Moving to a free trade agreement, a Norway-style arrangement, or remaining in the EU would all have very different implications for the UK’s sovereignty, prosperity and global influence. But there is something even more important to worry about.

The country is riven. Angry Brexit supporters harass ministers and MPs. And the Final Say campaign has shown it can turn out hundreds of thousands of marching Remainers, increasingly cross at being ignored. Brexit has divided families and friends and feelings are raw. The biggest challenge we face will be holding the country together, whatever the outcome.

Tensions are high because the government’s handling of Brexit has robbed it of legitimacy for three reasons. First, May’s deal has already gone down to defeat in parliament by a record-breaking margin, leaving her trying to ram the deal through with threats of economic calamity and bribes to biddable MPs with extra cash for their constituencies.

Second, since the current vision for our new relationship with the EU consists of just a few pages of fudge, parliament is being asked to commit to fundamentally reshaping our constitution and economy with little idea of what that final shape will be.

Third, with the prime minister likely to be ditched by her party in favour of a Brexit “true believer” once we’re out, her deal facilitates what in 2016 would have been considered the hardest of Brexits. Yet there has never been much evidence of a majority in the country for such an extreme interpretation of the referendum result. Brexit acrimony is certain to deepen if it goes through.

What is the way out? Neither hard Brexiters nor Remainers are likely to be convinced that they are wrong in their deeply held beliefs. But one thing reasonable people should all agree on is that for democracy to function effectively we need to find a way that people on all sides can accept the outcome. To achieve that, the process matters as much as the destination.

Achieving closure will require the government to address the problems with its current myopic approach. First it needs to stop the threats and coercion. For any deal to be durable, it has to have been approved by MPs on its merits. Second, the government must work with the European Commission to agree the major components of its preferred Brexit destination before we leave. Something the government should have spent the past year doing, this will now require a significant extension to Article 50. But no legitimate Brexit can be built on hoodwinking the public about what the future relationship will look like.

Finally, the ultimate deal will only stick if it is confirmed by a second referendum. Such a commitment will force the government to pursue a version of Brexit that’s likely to command broad support and prevent it being hijacked by fanatics as the process to date has been. But, crucially, ratification would also make it hard for subsequent governments to uproot the arrangement, putting the issue to bed for a generation one way or the other.

While hardliners have sought to undermine the idea, going back to the people at some stage is inevitable. Whether this year, next year, or after a decade of further exhausting argument, and dissatisfaction with our new relationship with the EU, the Brexit issue will not rest until the outcome, whatever that may be, is seen as legitimate.

The headlong rush to bundle the UK out of the EU by fair means or foul threatens the stability of our democracy. Pragmatic parliamentarians and leave-inclined Labour MPs should reject May’s short-term comfort blanket and reset the Brexit process if we’re to avoid poisoning our politics for years to come.