I have a dream. A dream of a decent night's sleep. Not necessarily the hallowed, undisturbed eight hours – the impossible dream if you will – just six consecutive hours would do nicely; I'm not greedy. But for most of last year, even that eluded me. For months I'd wake, heart pounding, in the dark pre-dawn hours for no discernible reason, soaked in sweat, unable to return to sleep. For months, that was, until I met the man of my dreams.

Guy Meadows is the best person I've ever slept with. I would say that he opened my eyes to an entirely new world – if it wasn't that he'd done exactly the opposite.

My name is Jonathan and – like 6 million other Britons – I'm an insomniac.

I haven't always been like this. For much of my life, I would sleep like an anaesthetised patient on an operating table. My friends jokingly nicknamed me "Somnio" for my "superpower" to sleep anywhere, at any time: sofas, buses, trains, even – on one memorable occasion – a round trip on a ski lift.

But about nine months ago, after a near-simultaneous one-two-three of major life events: getting married, buying our first home and a close family bereavement, somebody sneaked kryptonite into my pillowcase, and my superpower was gone.

Since then I had tried countless "solutions", from hot baths to a cold thermostat. I'd gone through three different types of eye mask and an entire menu of herbal teas. I had bought new pyjamas (soft) and a new mattress (hard). I'd even tried a brainwave-monitoring headset called a "Zeo", and slipped between the sheets looking like Rick Moranis in Ghostbusters. But however I approached it, the doorman at the entrance to the Land of Nod simply shook his head.

Cue Dr Guy Meadows, "The Sleep Doctor", who last month established the week-long Sleep School, on the Caribbean island of Grenada.

Now the first thing to note about Sleep School is that, ironically, it takes a good eight hours to get there. For the 90% of the population who do not suffer from insomnia, this might seem somewhat excessive. But to be candid – and I'd like to think I speak on behalf of the exhausted minority here – I would have flown to see the man in the moon if it meant I could start to sleep properly again.

The other 20 students, who had travelled from across the world for Sleep School's inaugural week at the start of December, obviously felt the same. Like me, they had exhausted all of their other options – pun entirely intended. 

The battle lines were drawn: our showdown with the sandman was to take place just a stone's throw from the beach at LaSource, an holistic resort on the sleepy south-eastern coast of one of the Caribbean's sleepiest islands.

"People have become very good at sleeping very badly," says Meadows, as we pull up wooden chairs for our first session, forming a rough semi-circle in the pavilion that will be our place of learning for the next five days. "Good sleepers don't have any rules. You ask them what they do to get to sleep and they'll say 'nothing'. You ask an insomniac what they do and they'll say 'everything'.

"Sleep is a natural physiological process. Our bodies know how to do it – we are just getting in the way."

Looking around the sundrenched pavilion as my classmates introduce themselves and their own issues, I have to confess I'm a bit wary.

Where are the shiny, state-of-the-art machines, the comforting leads, wires and computers to analyse our sleeping patterns and return them to normal? There isn't a single pot of pills in sight. All we're given is a 50-page workbook, with blank spaces for our homework each night.

Next to the pavilion, a small, splashing water fountain gurgles and chuckles to itself – possibly at the idea of 21 adults flying across the world to learn a skill that newborn babies manage with ease.

On first impression then, Sleep School is a cross between an AA meeting and one of those rare school days where the weather's so nice you get to have a lesson on the field. Except this time, nobody's nodding off at the back.

My fellow sleep-schoolers range in age from early twenties to mid-sixties and come from all over the world: the UK, the US, Germany, the Netherlands and Australia to name a few. But as we take turns describing our sleep issues, I'm struck by how similar we all are. Whenever somebody describes an experience, six or seven heads immediately nod in accord.

Clinical insomnia, Guy explains, is categorised as "three to four nights of poor sleep a week, lasting for more than a month". Looking round the room, I see straight away that we can all relate to that. The good news, he adds, is that we can all recover from it, too.

As if from thin air, Guy whips out a length of rope. Beckoning me to the centre of the class, he offers me one end of the rope, before gently pulling on the other, as if warming up for a bout of tug-of-war.

"What's your natural instinct when I pull?" he asks.

"To pull back," I reply, doing exactly that.

"Fine, but how much energy are you using in the process?" he asks me, as I place my feet shoulder-width apart, and feel my triceps straining. A lot. He's stronger than he looks.

"What if you simply let the rope go? How much energy would you be using then?" he asks. Obviously none. "So what do good sleepers do to get to sleep?"

"Nothing; insomniacs do everything."

This metaphor is at the heart of Guy' approach to insomnia. To win the battle once and for all, he says, we have to stop fighting.

His system – which he claims has an 87% success rate – is based on acceptance and commitment therapy (ACT). This is a process of "welcoming" your problems, accepting them and then watching them lose their power and drift away. It's diffusion by defusion.

"The harder you try to fight insomnia, the more you fuel it," says Guy. "Instead you need to embrace it. Think of it as a patch of quicksand: the more you struggle with it, the deeper you sink"

I'm not particularly convinced. Doesn't dropping your end of the rope mean you've automatically lost the bout of tug-of-war? But, I reason, at least this approach is something I haven't tried before. Plus, I'm sick of going to bed looking like Rick Moranis.

Guy, who has a PhD in sleep disorders, has devoted the past decade to this field, seeing more than 500 patients on a one-to-one basis every year. The majority come to him after trying a cornucopia of desperate remedies first, from lying naked on the kitchen floor to lying naked on a bed of nails (a lot of quack insomnia cures involve getting naked, it transpires). One of his clients had bought six new mattresses in the space of 12 months, while another – a city executive and mother of two – would wait patiently until her children and husband were fast asleep before slipping out of bed and tiptoeing through the house to smoke a joint of marijuana at the bottom of the garden.

"The real solution," repeats Guy, "is to accept the situation. And the best way to unlock that is by practising Mindfulness."

Through a number of targeted exercises – including the analysis of a single raisin in painstaking detail – he introduces us to this concept. In a nutshell, it is about becoming acutely aware of your immediate surroundings via your five senses. In this way, you become an "observer", distancing yourself from troublesome thoughts. Or, as Guy puts it "you move from the subjective into the objective, and from there, into sleep".

Sleep School consists of five two-hour classes over five consecutive days, and while it does seem somewhat flashy to fly to the Caribbean to experience it, there are a number of positives to tackling insomnia at a resort such as LaSource. First, every package includes a free massage or treatment every day, and guests are encouraged to join yoga or t'ai chi classes first thing in the morning. Second, you're in a group environment, which leads to a lowering of inhibitions and a ready-made support network. Third, you're completely shut off from any day-to-day concerns, and can fully focus on the study of sleep.

"This is the optimal learning environment – completely removed from the everyday stresses of life, with abundant relaxation all around you," says Guy.

It sounds corny, but he's right.

As the classes go on, a sense of camaraderie builds. We applaud quality sleep over breakfast, compare notes by the pool and discuss homework on the beach. This isn't just Insomniacs Anonymous – it's a full-blown fusion of summer school and pyjama party, and I'm genuinely enjoying it.

But despite this, and our increasingly fascinating exploration of polysomnography (the technical term for sleep study), I'm still struggling with the most important part of my homework: a good night's sleep.

One of the final parts of our course involves a detailed look at something called the amygdala: two walnut-shaped and sized bumps at the back of your head that are key to your brain's emotional function.

"Your amygdala evolved to notice looming threats, such as lions or tigers, then flood your system with adrenaline and cortisol to help you fight them," explains Guy. "It's like a rev-counter. The problem comes when you're under lots of stress, and your amygdala keep getting pushed into the red. If this happens too often, your body adapts and thinks it needs to stay there permanently. And that means your system is flooded with adrenaline and cortisol when it doesn't need to be." Like, say, when you're asleep.

This all makes perfect sense. More than that, it's reassuring to know that I'm not a freak; my walnuts are just a little … overactive. It's a revelation.

Then, on night four: a breakthrough. As usual, I wake up at about 4.30am, but before reaching for my iPod, accepting that I will not go back to sleep, I concentrate hard on being "present". On feeling the bed under my body, on the sound of the fan above me, on the ocean outside my balcony. And somehow, there's no jagged kryptonite under my head any more. The next thing I know, it's 9am and I've missed my yoga class.

The final day of Sleep School is incredibly positive. Almost everyone feels they have made progress of some kind, even those who have struggled with insomnia for more than 40 years.

Guy waves us off outside the resort, and it's as if he's casting one final spell: I sleep for the entire plane journey, all the way to London. Somnio is back. 

But it doesn't stop there. Soon after my return, I earn a "tenner": 10 hours of beautiful, undisturbed slumber. I wake from deep sleep amazingly refreshed and – bizarrely – with the detailed schematics of a bicycle for cats in the front of my mind.

In the four weeks since Sleep School, I've admittedly had a handful of mediocre nights' sleep, but predominantly they've been good, sometimes excellent – and never bad. Mindfulness and ACT aren't miracle cures, but they beat dressing like a Ghostbuster or sleeping on the kitchen floor. As far as I'm concerned, Sleep School was worth every penny. Plus, I tell myself, I can make the money back tenfold if I patent the Cat Cycle. Well, I can dream …

• The next Sleep School at LaSource (theamazingholiday.com) will run from 3-9 June. Kuoni (01306 747008, kuoni.co.uk) offers seven nights on an all-inclusive basis, including BA flights from Gatwick and transfers, Sleep School, six spa treatments, three dives (if you're Padi qualified), plus daily t'ai chi, yoga and watersports, from £1,689pp, based on two sharing. Further information at thesleepschool.org