Tuesday’s statement from the prime minister was another shameful moment in a Brexit process that has not been short of them.

We are used to the sight of Theresa May coming to the House of Commons and spending hours taking questions. What we have not had much of are answers. This was the case again when I asked her whether no deal remains on the table. It clearly is – despite parliament voting against it, and the views of her cabinet, ministers and sensible backbenchers.

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My colleagues and I in the Independent Group have spoken in the last week of how our politics is broken. Nothing better illustrates that than the sight of Theresa May refusing to rule out no deal, while Jeremy Corbyn ducks and dives around, trying not to commit to a people’s vote in a way that could actually make it happen.

It is worth remembering how we got here – the sorry saga of the last three years.

Take the prime minister first. She triggered article 50 without any clue as to what kind of Brexit could command the confidence of parliament or her party, and she did so without having any conversation with MPs or the country. Instead, the referendum result was taken as an instruction to deliver a hard Brexit, with the UK leaving the single market and the customs union.

That approach was put to the people in the 2017 general election. It was rejected. May lost her majority. Astonishingly, she ploughed on regardless, maintaining her red lines and trying to deprive parliament of having its say on her deal – until she was forced into it by members of what is now the Independent Group and my excellent colleague Dominic Grieve.

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Still, no progress was made, because the government did not have an agreed position on what it wanted from the negotiation – until Chequers. Then we had a collective view, until Boris Johnson and David Davis sauntered away from the mess they themselves created. The government kept on kicking the can down the road, delaying the vote on the deal time after time – until it went down to the biggest defeat in the modern history of parliament.

If it is a tale of tragedy on the government side, then on the opposition benches it is best described as farce. We all remember the referendum campaign that Jeremy Corbyn “fought”, and we do not do so fondly. His lacklustre effort was at best ineffectual, and at worst totally sabotaged the campaign.

The day after the result, he demanded that article 50 be triggered immediately. He adopted the same position as May on the single market and customs union, ruling out participation in either. During the general election he almost ignored Brexit completely – and then refused to change his position, declining to back a Queen’s speech amendment tabled by Chuka Umunna, which backed both (as well as, incidentally, calling for no deal to be ruled out).

Even when Corbyn moved, he did so through a fog of ignorance. He shifted to back a slightly softer Brexit, but only being part of a customs union with certain conditions, which Brussels would never agree to. He either didn’t know or didn’t care that there are countries that are part of the single market but aren’t in the EU, claiming that one necessitates the other (it doesn’t). He was dragged kicking and screaming towards the notion of a people’s vote, and ended up backing a ridiculous conference resolution that was falsely spun as progress when all Labour did was commit to the public having the final say as an option, not policy.

It has taken the resignation of eight decent members of his party for him to accept a move towards a people’s vote. Even then, it is stuffed full of terms and conditions. He has come off the fence precisely at the time when it may be too late for him to make a difference, and when he has shown so little enthusiasm that there could be 25 or more of his MPs who will refuse outright to back a referendum. Can there be any greater failure of leadership?

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In the Independent Group we are heartily sick of it all, and we know people in the country are, too. It is time for an end to these absurd gambles with the lives and livelihoods of our constituents. We have had another week of these two parties failing to provide direction. Another week of prevarication. Another week closer to the cliff edge. It has to stop now.

That’s why as a group, we have tabled an amendment for today’s Brexit debate that would pave the way for a people’s vote. It is supported by the Liberal Democrats, the SNP and Plaid Cymru. Any MP, from any side, who is prepared to put the national interest first must back it.

A week ago, Heidi Allen, Sarah Wollaston and I joined the ex-Labour MPs in taking a stand; in saying loud and clear that our politics is broken and that it has to change. Our problems go deeper and wider than Brexit, but Brexit is the biggest one we face – an existential crisis for our economy and our society, writ large thanks to the inability of our rotten parties to do their job.

High noon is about to arrive. MPs on all sides must now make their stand.

• Anna Soubry is a former Conservative MP who left to join the Independent Group