Enormous and smudged by dirt, the roof of canvas is supported by spindly masts of wood and guy ropes that hardly look a match for the early summer storm brewing just south of here. Yet it’s shelter enough for the thousands crammed underneath, weary but grateful for the shade. We are at a tent revival of sorts – and finally their preacher, garlands of flowers on his chest, arrives.

Clambering on the small stage amid a pandemonium of trumpet blasts and disco beats, Andres Manuel Lopez Obrador, is no messiah but merely a politician (though some among his supporters may beg to differ). He begins with an apology that sounds also like a boast. “I wish I could say hello to all of you by hand,” he says, “but this has grown so much I can’t do it any more.”

And so it has. This dusty sports field on the outskirts of Tecamachalco, 30 miles east of Puebla, is the third of four stops on this single day for Mr Lopez Obrador as he makes his third bid in 12 years for the Mexican presidency. As this country of more than 125 million people prepares to go to the polls on 1 July, it’s a quest that this time seems to be on course – something he is also happy to point out. “The rice is cooked,” he pauses to tell his supporters. It’s a done deal.

There is no such thing in the democratic process, especially in a country where vote-buying is a virtual tradition and strange-bedfellow alliances can be struck at the 11th hour. Yet polling shows Mr Lopez Obrador, known everywhere here by his initials, AMLO, surging so far ahead of his two rivals, José Antonio Meade and Ricardo Anaya, it’s hard to see who or what could stop him.

A forecast by El Pais, the Spanish paper, based on several polls already published, gives AMLO almost 50 per cent of the vote and a 92 per cent chance of being the next president, over a 7 per cent chance for Mr Anaya, leader of the right-left ‘For Mexico to the Front’ coalition, and 1 per cent for Mr Meade, of the governing Institutional Revolutionary Party, PRI, who leads his own coalition.

Victory for AMLO, who heads his own ragtag National Regeneration Movement, or Morena, would spell an abrupt, potentially shocking, reordering of Mexico’s political landscape. The magnitude of it will depend on which AMLO ends up wearing the presidential sash. Some expect a more moderate and pragmatic leader to emerge, far different from the out-with-the-elite firebrand of the campaign trail. Others see a populist authoritarian with statist economic tendencies who might do to Mexico what Hugo Chavez did to his once-prosperous Venezuela.

Those with most to lose from a sharp shift to the left may harbour the deepest fears. In the smarter neighbourhoods of Mexico City, like Polanco, there’s chatter of fleeing the country if he wins. “I still sleep at night,” one young man says, “because I have an American passport.” His nervous laughter leaves the comment somewhere between a joke and a threat. Anecdotes are exchanged of young, rich Mexicans spending small fortunes on visas to allow them to bolt overseas.

As mayor of Mexico City from 2000 to 2005, AMLO spent heavily on expanding social programmes, particularly for the most needy. This policy allowed him to leave his job with an approval rating of 84 per cent. His attempt to bring the same leftist vision to the presidency in elections in 2006 was thwarted when he lost by a narrow margin to former President Felipe Calderon of the National Action Party, PAN. He tried again in 2012 and lost by a wider margin to Enrique Peña Nieto, the PRI candidate and now the outgoing president.

His detractors, who hoped they’d seen the last of him, never forgot what followed his 2006 loss. Convinced victory had been stolen from him, AMLO summoned tens of thousands of his supporters to the capital’s historic centre for a traffic-crippling mass occupation that lasted for months. Critics saw not just a sore loser but one with a dangerous disregard for law and order.

If any among them had come to the Tecamachalco revival, they’d hardly have been reassured. The stump speech that has propelled AMLO to so commanding a position is an unbridled symphony of populist class-baiting and anti-establishment rabble-rousing. He vows destruction to the “power mafia” of Mexico, starting with all the previous presidents whose pensions he will refuse to reauthorise. He’ll ditch the new presidential plane purchased by Peña Nieto, and sell off his fleet of helicopters as well, except for a few he’ll turn into air ambulances for the poor.

Parents bring their children to the Tecamachalco rally to cheer on AMLO (David Usborne)

Barely hitting his stride, AMLO ploughs on with pledges to slash the salaries of senior-level government civil servants and boost those of soldiers and policemen. He vows to eschew the presidential palace, Los Pinos, calling it a haunted house, and to conjoin its grounds with neighbouring Chapultepec Park in Mexico City, to make a single 600-acre green space for everyone. “Not even New York, Paris or London have a park as big as this,” he declares.

His economic agenda, though always short on specifics, follows a not dissimilar tack. He has spoken of price controls for farm produce and state intervention to make Mexico self-sufficient in food. At this meeting, as at every stop, he airs his distaste for the privatising of state assets, notably, under Peña Nieto, of the oil industry. “Look up what privatisation means,” he tells the rally. “Privatisation means making something that is public private, and I won’t do that any more.”

That has sent tremors through the business community, as have mutterings, but not more, of cancelling construction of Mexico City’s new international airport, designed by Britain’s Norman Foster, already under way. It is due to open just east of the capital at the end of 2020. Meanwhile, the candidate has mused with still greater vagueness about exploring the use of amnesty laws to break the cycle of violence from the war on drugs and the cartels.

Under the canvas, they like what they hear. “There is more poverty now than ever before,” notes Francisco Perez, 52, a photographer of society events that barely seem to happen any more in Tecamachalco, a town that in recent times has seen growing levels of violence. “There are no jobs, so more people commit crimes to get by. It is only getting worse.” Diana Luna, 24, who works in an office, weeps as she walks from the rally to go home. “He is the hope we need. He is the change we need, because we are so fed up,” she says. Every member of her family will vote for AMLO, she says, almost implying they no longer have any choice.

If it turns out to be third time lucky for AMLO, it may be because he is pushing at an open door. In 2000 voters dumped the PRI for the first time in decades, hoping that by choosing Vicente Fox of PAN they’d see change. By most accounts they saw none. Or none they recognised. They gave his party a second chance in 2006 with Calderon, whose presidency is now widely associated with a war on cartels that cost 60,000 lives in six years and still rages. After reinstalling the PRI by electing Pena Nieto, voters have seen a succession of corruption scandals – the “cancer of Mexico” in AMLO’s words – and persisting poverty and violence.

At this point, just about every Mexican knows change has to come. Yet somehow it appears to be AMLO who has done the best job presenting himself as the candidate who can deliver it, never mind his advanced years – he is 65 in November – or the the curious mix of advisers around him, some from the Christian far right and others who have migrated from the old PRI. “The secret of Andres Manuel is that he has been almost 18 years travelling all around Mexico,” comments Frederico Martinez, a writer and former civil servant who is an occasional, informal adviser to the AMLO camp. “And I mean he goes to the last corner of the country and he sits down and he talks with the people and he knows how to listen and how to talk to them. He walks and he talks. He doesn’t have bodyguards, people love seeing him.”

“It won’t be his victory, it will be because the country has moved,” notes an adviser to Mr Anaya who asks to remain anonymous for fear he would be accused of conceding defeat before it happens. “It isn’t that he has changed, the country has changed. He has gone through the country, he knows the grievances and he is mostly right about it.”

The same adviser shares the fears still quietly expressed in the salons of the capital – it is telling how few people are willing to shed their anonymity to speak about this election – of AMLO taking on dictatorial airs. “This is the perfect recipe for an authoritarian regime. People are angry, the inequality, anger against the outside, a totally uncontrolled security situation, and an extremely charismatic leader with people around him who don’t really represent anything.”

Leftist frontrunner Andres Manuel Lopez Obrador addresses supporters during campaigning in Nuevo Laredo (Reuters)

Those fears will surely be sharpened if Morena, his party, wins a majority in congress and a swathe of state governorships as the polls also suggest, providing him leeway possibly to tinker with the constitution. “People should be cautious, they should be afraid,” one global business leader based in Mexico City says over a tasting-menu luncheon in one of the capital’s most exclusive hotels on its grandest avenue, the Paseo de la Reforma. “I will tell you why. He is going to take congress, the senate and the presidency – and that’s why we should be afraid.”

For a while something close to panic gripped the high floors of Mexico City’s gleaming towers. Some corporations were accused of trying to steer employees way from AMLO; among them, according to Bloomberg, the mining colossus Grupo México, supermarket group Chedraui and the airline, Aeroméxico. Employees at El Palacio de Hierro, an upscale department store chain, were treated to a company video telling each one of them to “inform yourself and reflect before voting,” while a graphic exhorted them not to vote for any single candidate “out of anger”. The company denied it was trying to influence how anyone on their payroll actually voted.

Guillermo, an apricot vender, likes AMLO but is unsure if he trusts him (David Usborne)

Perhaps aware they were providing AMLO with ammunition for his assaults on the elite, many business leaders have since tried to open communications with him. Earlier this month he met with members of the Mexican Business Council, which presented him with their own plan for the country’s economy over the next decade. There are some among their ranks who just think that the fearmongering about him has gone too far.

“We have suffered major crises before and we have come out stronger,” notes Piero Gaudiano, chief of Mexico’s largest private jet fleet, Across, who also attended the private hotel luncheon. “I think it’s just going to be the same. It takes a lot more than six years to change how things are, but two minutes for them to get worse. I am hoping that he really intends to make Mexico better. That is what I hope.” He pauses and adds: “Though I am not sure.”

A few still dare imagine that AMLO may stumble and Mr Anaya will stage a last-minute surge – another says here that “rice cooked too early risks going bad” – but it doesn’t seem likely. In which case, any suspense left will be about which of the AMLOs emerges once he is in office. Will he moderate his positions or, like Donald Trump, use every promise made on the campaign trail as guide posts for his presidency?

As the revival tent empties, a short man named Guillermo pushes a squeaky cart piled with fresh apricots. (They are surprisingly devoid of taste.) He has been listening to AMLO and seems pleased with all of the promises he has made. He will be good for farmers, he offers, and will lower petrol prices. But does he think AMLO will actually do as he says? Will he practise what he preaches? He wrinkles his nose and looks down: “Hmm, I don’t know.”