In the conference room of the Jurys Inn hotel, delegates bought and sold flat Earth merchandise, which included "Flat Power" T-shirts, flat maps and, of course, novelty spirit levels. Flat Earthers came from a wide variety of backgrounds and included smartly dressed IT consultants as well as off-grid environmentalists. In discussions held over three days, guest speakers unveiled their scientific "proof" that Earth is more pancake than profiterole. "My research destroys Big Bang cosmology. It supports the idea that gravity doesn't exist and the only true force in nature is electromagnetism," explained David Marsh, a manager at the NHS Supply Chain head office in Alfreton, Derbyshire. Marsh has carried out his own year-long research in his back garden, tracking the movement of the moon across the sky using a mobile phone app and a Nikon camera. His experiments have disproved, he says, the accepted laws of planetary motion. The convention's organiser, Gary John, said the event had been driven by a surge in interest in an idea that was thought to have flatlined at least half a millennium ago.

"People are waking up," said John. "We're seeing an explosion of interest in flat Earth theories and increasing mistrust of governments." During the past five years, online searches in Britain for the phrase "flat Earth" have risen tenfold, according to Google Trends. Over the same period, Facebook groups and YouTube accounts promoting the flat Earth theory have gained tens of thousands of followers. Then there are the prominent deniers with internet disciples. They include Kyrie Irving, one of the stars of US basketball, who repeatedly insisted that Earth was flat in a podcast in February 2017 that went around the world - or at least would have done if the globe was basketball-shaped. Though there are disagreements among the new wave of enthusiasts about just how Earth looks, most share a core belief the planet has no curvature, and is not moving through space or spinning. Participants revelled in attending a conference where they could express their beliefs without being ridiculed. They were prone to shouting out supportive comments and periodically broke out into loud laughter and jeering as convention speakers played NASA videos and speeches by world leaders.

While, historically, sailors might have feared sailing off the edge, modern-day flat-Earthers scorn such foolishness. "We know that continuous east-west travel is a reality," said the convention speaker and expert Darren Nesbit. "No one has ever come to, or crossed a physical boundary." Nesbit himself believes he can explain why no sailor would ever fall into the abyss. He calls it the "Pac-Man effect". In his theory, celestial bodies are able to teleport from one side of the planet to the other when they reach the horizon - just as the characters in the video game Pac-Man arrive on the right-hand side of the screen as they exit the left-hand side. "One logical possibility for those who are truly free thinkers is that space-time wraps around and we get a Pac-Man effect," he told the convention.

The shape of Earth is another topic that is fiercely debated. There are those who propose that it could be a circle surrounded by ice walls. Others believe that the planet has a domed roof; some suggest it is made up of a series of interlinked rings. Nesbit's own view is that it is supported by pillars and shaped like a diamond, with the North and South poles in opposite corners. "I'm not saying this is definitely what is going on, but I think it is a plausible model," he said. Sean Connors, a speaker at the conference and an employee at a school for children with special needs, said he began to question mainstream media narratives after the build-up to the Iraq war. "I believed [former prime minister] Tony Blair when he told me there were weapons of mass destruction in Iraq," he said. "When I realised that the government had misled me - that was a turning point."

John said: "We're not saying we have all the answers, but everyone here is united by the knowledge that the Earth is not a globe." The Telegraph, London