Former Tate Modern director Vicente Todolí founded Todolí Citrus Fundació to preserve rare citrus varieties and compile a catalogue of farming knowledge to inspire future generations.

Our preconceptions of lemons are very rarely challenged. But on a crisp November morning on Spain's leafy Valencian coastline, Vicente Todolí is showing me the secret side of citrus – and it's unlike anything I've seen on supermarket shelves.

The most weird and wonderful specimens are arranged on a table in his Sun-soaked orchard. There's one shaped like an octopus with fat tentacles, a wart-covered citron the size of a newborn baby and a colourful pear-shaped fruit splattered in a tie-dye of green and yellow.

They're not at all what I was expecting, and they're not entirely safe, either. "You will get burned," Todolí warns, pointing at a grass-greenbergamot. The oil is phototoxic, causing the skin to burn if it's exposed to UV light (it isn't dangerous to eat, but it is very acidic). "Want to taste?" he asks. I hold a slice up to the sun and eye it suspiciously; the golden segments light up like a stained-glass window. I tip my head back and squeeze drops into my mouth, being careful not to touch my lips. Eye-watering acidic needles stab my tongue. I'm reeling and wiping away tears, but Todolí is already on to the next fruit, squeezing the pearly contents of a finger lime into my hand. The little balls pop like lime-flavoured caviar in my mouth.

There are hundreds more unusual fruits to try at Todolí Citrus Fundació, a not-for-profit farm dedicated to researching and preserving rare citrus varieties. Hidden on a sleepy street in the town of Palmera, this is Todolí's passion project. He was born and raised on this farm, going on to study art history before serving as director at esteemed galleries such as Tate Modern in London and Milan's Pirelli HangarBicocca, where he works today.

Now, Todolí considers himself a fifth-generation orange farmer. He's fiercely protective of his old family farm, which is one of the reasons Todolí Citrus Fundació came to be. In 2010, a project was launched to raze Palmera's orange groves to make room for real estate. He tried to derail it through official channels and lost. "I was called a romantic enemy of progress," he recalls. But Todolí did not desist. Changing tack, he began buying plots of land. Some were abandoned patches of weeds and others were established orchards. He acquired around 4.5 hectares in total, an impenetrable fortress of precious farmland. "When I started it was a matter of urgency, I had to save the land," he says.

Around the same time, Todolí was working as cultural advisor to Ferran Adrià, former head chef of the iconic (and sadly closed) El Bulli (once-billed as the world's best restaurant). One day, the pair visited a garden on the outskirts of Perpignan which had more than 400 types of citrus trees, some exceedingly rare. The south of France is a little too chilly for citrus, so the trees are planted in pots. In summer they bask outside, and in October the gardeners heave them into a greenhouse to keep warm. During their visit Todolí asked, "How is it possible that they have done this amazing project with citrus, and in my area no one has done it?" Adrià replied: "Why not do it yourself?"

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