Democracy abhors a vacuum. The realignment that is happening now in our politics is the inevitable consequence of 62% of the electorate feeling politically homeless. A majority of our people who feel that neither of our main parties share their values, principles and integrity.

The decision of Heidi Allen, Anna Soubry and Sarah Wollaston to join the existing Labour members of the Independent Group begins what I hope will be a process that will finally give a voice to a so-far silent majority of voters. I admire them for beingwilling to put their heads above the parapet, to defy the onslaught of abuse I know too well, and to be brave enough to look beyond a vote taken nearly three years ago and to acknowledge the clear and present danger Brexit now poses to the livelihoods, jobs and quality of life of both leavers and remainers.

This is, as Soubry has said, is about so much more than Brexit. The antisemitism in the Labour party, the Islamophobia in the Conservative party, and the thuggish new tone to political discourse have all combined to alienate vast swaths of the electorate.

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Ordinary, decent citizens are sick, too, of the new deprivations that each day they are now being expected to reconcile themselves to in the name of Brexit – deprivations never spelt out during the referendum campaign. They see only too clearly how the best interests of constituents are less important to all too many of our MPs than the best interests of their parties. Jeremy Corbyn scolded Theresa May in Prime Minister’s Questions today for paying no heed to the economic slowdown, but Labour voters can see that Corbyn, in effectively backing May on Brexit, is aiding and abetting her in precipitating that slowdown, and failing to do his job as leader of the opposition.

It must be plain to Tory voters that theirs is no longer the “party of business”. One that under Margaret Thatcher promised international investors, such as the Japanese, that if they put their money into the UK they could be confident they would get in return access to the EU marketplace via a customs union. Instead they hear Boris Johnson, the former foreign secretary and a potential party leader, saying “fuck business”. They wonder, like traditional Labour voters, what their party now stands for.

It is obvious to voters that Brexit has caused both of our principal parties to take leave of their traditional and historic purposes and principles, if not also their senses.

I believe there was never a huge amount of difference between “one nation” Tories and traditional Labour supporters – that is why, for instance, the great Labour city of Liverpool is proud to number Michael Heseltine as one of its freemen. It was difficult not to be moved by the obvious warmth with which the Labour MPs who started the Independent Group greeted their new Tory recruits in the Commons. What they clearly share is, above all things, a love of their country. Some expected them to raise their voices loudly in their first PMQs, but I thought their silence spoke volumes.

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I have tried with myLead Not Leave campaign to offer constructive solutions to the current impasse we are in and that was why earlier this month I delivered a letter to May suggesting she took up the promising negotiations that her predecessor David Cameron had begun with Donald Tusk some months before the referendum vote.

My hope for this new group is that it, too, can take a constructive approach and that its members can continue to put aside party politics and egos and work together in the national interest. The Sky Data poll after the new grouping was announced showed it had got off to a flying start – with a 10% share of the vote – but it was hard not to see the crying need for it to get together quickly with the Lib Dems (on 9%) and other like-minded groups to overtake the Labour party – 26% to the Tories’ 32%. We, the people, now require real opposition on the defining issue of our times. We need to accept our old politics is no longer fit for purpose. Changing membership rules in both the old parties has resulted in more extreme elements coming to the fore with agendas and aims at odds with the vast majority of the memberships. It is no longer good enough when our local MP and the most senior people in the parties we normally vote for are at best ambivalent and at worst contemptuous of our views when the hours to 29 March are ticking down so rapidly.

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With real determination and courage, there is still no reason why, even at this late stage, both of our political leaders cannot save their parties by facing down the well-organised and well-funded special interest groups within them. The obvious first response to the ructions they must both now be feeling is to allow their MPs a free vote on Brexit. With no emerging majority in the House of Commons, a public vote seems highly desirable, but, short of that, they must let parliament do what parliament does best, which is to put the interests of the country first.

I welcome the Independent Group as it is committed to saving the country from a catastrophic hard Brexit. That, for now, is good enough for me, and, I suspect, for a great many others.

• Gina Miller is the founder of Lead Not Leave

• This article was amended on 21 February 2019. The Sky Data poll after the new Independent Group was announced showed the Conservatives had a vote share of 32%, not 23% as an earlier version said.