"You are going to meet Martin Strel?" a woman says to me in Ljubljana.
"You know who he is?" I ask.
"Yes, of course. He is famous in Slovenia … But a lot of people here think he is a bit weird."
That doesn't surprise me. I know about Martin's epic river swims, which have included passing dead bodies in the Yangtze, and I've seen the film Big River Man, which charts the bouts of drinking and madness that punctuated his 66-day progress along the Amazon in 2007.
"But weird in a funny way, right?"
"No," she says. "Just weird. We are not sure why anyone would want to swim in all those dirty rivers. We think he does it just to be famous."
I will soon have the chance to judge for myself. Martin's son, Borut, who masterminded the Amazon swim, runs a new company organising swimming expeditions, and I'm joining a trip in the Strels' native Slovenia. Six of us arrive one evening at Hotel Jezero, on the peaceful shore of Lake Bohinj in the Julian Alps: Tom from London; Giovanna and Kelly from Kent; Isabel from Wiltshire, who has just done her A-levels; and her mum, Emma. We're all confident swimmers, but as people discuss their experiences of 10k events and triathlons, I realise the scale of the challenge. My longest continuous swim so far is one mile, considerably less than the distance we will be covering each day.
Martin arrives after dinner. Stubbled and attired in shorts and T-shirt, he emits an aura of ease, at odds with his legendary toughness. He greets us warmly, apologises for his lateness – he's been having a catch-up chat with the Slovenian president – and gives a presentation about his past swims in heavily accented, scatter-gun English.
But it's not until next morning, as Martin gives me and Kelly a lift to our first swim at Lake Bled, that we get a real glimpse into his character. He attaches an innocuous-looking plastic clip to the steering wheel of his car. "If you use this, you save a lot of gas," he says. Intrigued, Kelly asks him how it works. "Energy," replies Martin.
As we digest this, we pass the former residence of President Tito, and then the lake itself comes into view: wide, clean and still. On an island at its centre sits a chocolate-box church, which will be our first destination.
Handing out neon-coloured swimming caps, Borut explains that he and three other guides will accompany us in kayaks, while Martin will be in the water. With his huge build, bushy eyebrows, and a large piranha bite scar on his back (apparently, it feels "like fire" when they attack), Martin should be an intimidating presence, but I feel reassured. The water feels cold, though, and I find it difficult to establish a rhythm.
"A lot of people are anxious on the first swim," says Borut when I eventually clamber ashore. "But as soon as they finish it, they relax."
We refuel with dried fruit, nuts, wafer biscuits and hot chocolate. Then, as a party of bemused Australian wedding guests arrive in gondolas, we leave. We swim around the island, back to where we started, and then, after lunch, tackle the full 2km length of the lake. As we reach the far shore, we realise that we've attracted a small crowd of spectators.
"Are you guys in some kind of competition?" asks a man.
"No. We're on holiday," we reply.
He seems confused. "You guys live around Lake Bled?"
"No, we're from England."
We swim on: a short burst to Lake Bled's lido, with sunbeds and showers. Here, we can rest, as the sun begins to set over the green hills.
The next morning, we drive up into the mountains, where we will cross the Italian border to swim in Lake Predil.
On the way we pass Mount Triglav (2,864m). "There is a saying that you are not Slovenian until you have climbed it," says Sasha, one of our guides, who first scaled the country's highest peak when he was five.
Martin expands upon his quasi-mystical worldview: my blue T-shirt has good energy, my black jumper not so much. Lake Bled's energy is strong, though Bohinj's is more powerful still, and our current location is exceptional. "This is a very special place," he says "People here live for 90, 100 years."
After Lake Predil, we return for a short dip at Kozjak waterfall. The icy water and tumbling stream encourage an atmosphere of elemental fun. Mido, the photographer accompanying us, says he overheard an Italian family discussing us, but the only words he could make out were "primitive tribe".
Back in the van, as we descend the Soca valley, I bask in the clear-headed exhaustion that follows cold water immersion. Limestone in the river turns it a cloudy, luminous cyan. Its rapids make it popular for watersports, but at a peaceful stretch we swim for 2km through the Caribbean blue.
This swim seems unexpectedly easy. Either the current's helping me, I think, or I'm getting better. But the next morning sees our final and hardest challenge: 4km across Lake Bohinj. We take a cable car up a mountain and look down on the glassy, dark blue expanse. If the boats seem small, we think, how much punier still would a fluorescent-capped swimmer look, inching across the vast lake?
My shoulders ache, and I'm tempted simply to lie down on the shore in the morning sun – but it's too late to pull out. I start, and soon find myself seemingly alone in the middle of the lake. I begin watching my own thoughts, remembering how Martin said he could hypnotise himself in the water. The guides tell me to move over and I laboriously correct myself, reaching the warmer water on the lake's edge to join the others.
And, suddenly, that's it. We say hasty goodbyes and, in a Mazda emblazoned with a picture of himself, Martin drives me back to Ljubljana, where he insists that I meet his nutritionist. Like Martin, he carries a small pendulum which can apparently assess energy levels, and, based on its information, he concocts a tiredness remedy for me.
Like much about Martin, I find the mixture a little hard to swallow. But Martin's faith in the power of nature is well-founded. Over three days in Slovenia, I swam further than I had ever done before, repeated that distance several times, and then doubled it. Had I been in a chlorine-ridden indoor pool, I'm not sure I would have found the energy.
• Strel Swimming Adventures (strel-swimming.com) runs trips to Slovenia from €498. The next three-night trip starts on 7 September. EasyJet (easyjet.com) flies to Ljubljana from Stansted from £40 return
