One million. This really is quite a number for a petition asking for a Final Say on the Brexit deal. Even if modern-day petition signing is easier now than in the days of pen and paper, it is quite something for a million people to take the trouble to express a view in this way. Are you listening, Theresa May?

The prime minister, no stranger to clunky sound bites that fail to stand the test of time, dismisses the People’s Vote campaign for a referendum on the outcome of the Brexit negotiations as “a politicians’ vote”.

Even by her standards – with “Brexit Means Brexit”, with “red, white and blue Brexit”, “strong and stable”, and “every vote will strengthen my hands” (oops) among her greatest hits – this is a particularly odd one.

It is precisely because of the shortage of politicians who have stood up for the genuine national interest, or even what they actually believe about Brexit, that the People’s Vote and The Independent’s Final Say campaigns have gone from a standing start a few months ago to become a movement capable of drawing almost three-quarters of a million marchers onto the streets of London this month.

Of course, there were politicians at the march, too. London mayor Sadiq Khan was there, and spoke well. Scotland’s first minister Nicola Sturgeon sent a well-judged video message, which put her nationalism second to the national interest, expressing her belief that the public must be given the right to pass judgement on whatever outcome Theresa May reaches in the tortuous, seemingly never ending negotiations. She believes the public has the right to make sense of what the British people voted for, after a miserable campaign won by Project Lies Over Project Fear.

There were five MPs of five different parties who had a united message. They said that Brexit was a developing disaster and the country had to have the chance to take another look, given how far removed we are now compared to what was promised. And where we are now is facing a wretched, holed below the waterline Brexit.

Labour’s Phil Wilson, alongside Tory MP Sarah Wollaston, said they were not prepared to support something they know will make their constituents poorer. If only more of their politician colleagues joined them, especially those of the Labour variety trying to pretend to themselves and, worse, to their constituents, that Brexit won’t turn out as bad as we are anticipating. They know, deep down, Brexit is being led by a right-wing, Johnson-Farage-Rees-Mogg-Gove coalition that will hurt the poorest and weakest most, and potentially be the death knell for the communities they are elected to represent.

Among the marchers I also spotted a handful of MPs and councillors, mainly Labour and Liberal Democrat, as the vast crowds inched from Park Lane to Parliament Square.

But a “politicians’ vote?” Please, prime minister, at least try to keep it credible.

Those 700,000 people were of all ages – the oldest I met was 92 – all backgrounds, all classes, all regions and nations of the UK. There were people who had voted for all the main parties and, crucially, thousands who had never voted at all because they were too young to have had a vote on 23 June 2016.

Most were there because they feel let down and unrepresented by politicians on both sides who are in charge of the most important set of decisions of our lifetime. On one side is May, who, like her predecessor, puts the party interest all too often ahead of the country’s. On the other is Jeremy Corbyn, for whom Brexit appears to be a gigantic elephant in the corner of a room otherwise filled with well-meaning plans to end austerity, without reference to the fact the elephant will trample all over them should he become prime minister of post-Brexit Britain.

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Theresa May, the politicians’ vote is the one you hope to be able to win when you scrabble together a deal during our divorce from Europe, with the tough stuff kicked down the road of transition and beyond. The politicians’ vote is when you hope Tory MPs lack the courage to challenge you, and enough Labour MPs fall for the lie that yours is the only alternative to a ruinous no-deal Brexit favoured by some in your party.

The People’s Vote and the Final Say IS the alternative. The 700,000 who marched, and the million who have signed The Independent’s petition, are two very big signs that, for all your insults, the issue is not going away. It is the politicians who are making a mess of Brexit and so making a global laughing stock of Britain. It is the people, and our campaign, who are offering you a way out of the mess you have created. You would be wise to listen.

Given the numbers involved, you can’t say you haven’t been warned.