“Please do not waste this time.” That’s good advice to his vassals from our kindly overseer, Donald Tusk, who has done all he can to save us from ourselves. This broken country has been given six months’ injury time to try to recover from our self-inflicted concussion. What is the chance of that happening?

This gift of time should be a chance to step back, start again and restore our wits and our equilibrium. Imagine how some subtle and wise prime minister might set about mending the country. This would be time for a series of citizens’ assemblies around the country, deliberative councils and debates laying out the alternatives and the facts, slaying the fictions once and for all, leading to a referendum to let voters decide what parliament cannot. The electoral commission says the 31 October deadline allows just enough time: let them better police the next process to stamp down on abuse. Employ the independent organisation Full Fact as arbiter of accurate information.

That’s what Theresa May should be ready to announce today. But if she were that wise and subtle leader, Britain wouldn’t be in this appalling state. Instead, her deranged party will set about trying yet again to replace her with an even more divisive and destructive no-deal rightwinger. Kenneth Clarke on the Today programme this morning rightly called this the “daftest diversion”. A more extreme Brexiteer promising a hundred impossibilities to get elected, will face all the same dilemmas, the same deadlocked Commons, whose only majority will be to stop him (it won’t be a her) pressing the nuclear no-deal button he will have promised. On a steep learning curve about realities, he will have to eat his words, the clock ticking away more wasted time.

May is determined to see a deal through. Clarke thinks his customs union compromise can squeeze through. Both seem to think another series of blighted knife-edge votes can resolve this. It can’t. Some fluke of a majority, inched across the line will still leave both sides enraged. It will never be “real Brexit” for the insatiables. The remainers, now in the majority according to all polls for over a year, will rage against any undemocratic Brexit imposition. Only abandoning Brexit has any hope of restoring calm. Those who just want to “get it over” need to hear that Brexit is a never-ending process that will dominate UK politics for eons. The only “over” is the people choosing to stop all this.

Polite cross-party talks will last just long enough to keep up the pretence there was ever the remotest chance of agreement. Even if Labour were offered all it asked for – that won’t happen – reasons to refuse would be found because if Labour enabled any kind of Brexit the party would be over. Brexit is the madness of a small group of Tories who infected their own party and the country: Labour has to be the national doctor curing the country of this disease.

May is not done yet: she still has ammunition in her locker. The Tories can’t avoid a hammering in the local elections three weeks away. If they still refuse her deal, or her deal plus Clarke’s customs union, do they really want to go into European parliament elections to face virtual extermination under a PR system that favours Ukip and Farage’s Brexit party? The ERG seem happy with that.

By all laws of opposition, Labour has to stand in the European elections as the remain and referendum party or, if they prevaricate, face a well-deserved walloping by the Greens, Liberal Democrats and Change UK. Both parties risk possible extermination. A ComRes poll this week exploring acceptable options found 40% willing to revoke article 50, as Tusk still hopes for, 38% would accept a no deal and 38% a referendum. European elections in May will become a proxy referendum, and the results will make an even stronger case for an actual referendum. The only chance May’s deal still has would be with Labour agreeing to nod it through in exchange for putting it to a confirmatory public vote.

We must stand back from all this mayhem and political misery with its Halloween deadline – that Tusk says can be extended yet again. Now, in this pause for thought, is the time to build a groundswell for a review of the constitution. When this is resolved, probably by staying in the EU, it will be the right time to reform an electoral system that makes no sense.

How can voters put an X in the Conservative box with no way to saying if they are a Clarke-ite or a Mogg-ite? Or vote Labour with no say if that’s for Chris Williamson’s aggressive Corbynism or for those he attacks as “Blairites”? Time for Lords reform and a review of the badly drafted fixed term parliament act, and much more. This needs a rare royal commission to examine the entrails of a political system that has failed the country in this crisis. At least some good should come from all this wretchedness.

• Polly Toynbee is a Guardian columnist