It was a warm winter morning in Marrakech and I was staring at a middle-aged man called Steven and urging myself to fall into his arms. "Just let yourself go," he said. "I can't, I just can't," I whimpered. "I'm scared – I have never done this before." "You can," urged Steven with persuasive authority. "You just need to let yourself relax."

I took a deep breath, summoned up what willpower I had and let myself fall. Into the heated swimming pool. For a few seconds my feet were off the ground and I was floating before Steven caught me. "That was great," he said, "I think we'll have you swimming by the end of the week."

I am a non-swimmer. I fell into a swimming pool during a lesson when I was 10 years old and was so traumatised that I refused to join in any more lessons. I didn't think I was missing much since my family never went on holidays when I was young and as an adult I have always preferred city destinations to beach holidays.

In the past that hasn't mattered but last year I married a woman who loves water so much I suspect she is a mermaid who has had the snip. I want to be able to swim in the sea with her, which is why I decided to go to Marrakech for a week-long swimming holiday led by Steven Shaw. Steven has taught 15,000 people to swim using a method based on the Alexander Technique.

There were 12 of us in the group – ages ranged from 39 to 80 – and our week at the Kenzi Farah Hotel began with an early morning session sitting in a large circle. Steven asked us all to introduce ourselves and then talk about any bad past experiences with the water. Listening to everyone share their stories it felt like I had joined AA – Aquatics Anonymous. Everyone apart from me could swim to some degree: they were here to improve technique or stamina. We talked about our hopes for the week. One man said he wanted to be able to swim with his head under the water, while a woman in her sixties talked about wanting to venture out of the shallow end without having a panic attack.

Then it was time to take the plunge. We made our way to the pool for the first of our two daily sessions. These were to be supplemented with individual lessons in swimming and Alexander Technique. Steven began by telling us to walk in the water. Next we had to crouch in the water, our arms in front of us and he told us to slide our feet backwards in the pool: an aquatic moonwalk. Once we were all comfortable in the water Steven tried to teach me to float. At his command I put my head in the pool, kicked off from the edge and let my hands float in front of me. And somehow, magically, I found that I was actually floating. It was a moment of indescribable joy, like learning I could fly.

That evening the group ventured out into the heart of the old city, the Djemaa el Fna. The square throbbed with noise, the cries of stallholders selling spices and dried fruit, the drone of motorbikes and the babble of snake charmers. We found a restaurant that overlooked the square and had a terrace from where we could admire the chaos as I ate my fish tagine. Shaw's company also runs courses in Britain, but being able to explore Marrakech's markets and restaurants was one of the great advantages of learning to swim in Morocco.

The next morning began as usual with a session on land where Steven led us as we practised our strokes in a large circle. He instructed us to hum, first with our heads bowed, then looking straight forward. It was meant to show how our breathing became tighter when our heads were pointing down but I was distracted by the gawping hotel guests, who must have assumed that we were members of some weird cult, with bald-headed Steven as our Messiah – the buddha of the breaststroke.

In the pool the competence gap between the others and me was so stark I was singled out for individual attention. I thought I was doing well until Esther-Clare, a 72-year-old former midwife from Edinburgh, paddled up to me and asked, "Is there something wrong with your legs? I mean you don't look disabled, so why are your legs so crooked in the water?"

The next few days followed the same routine: early breakfast, a session on land and then a full day of lessons. The more time the group spent in the pool, the bar and the city, the closer we became. Having to admit to fears and vulnerabilities meant opening up to each other with distinctly un-British speed. Esther talked movingly about what being in the water meant to her. "I feel like I am a young girl when I am in the pool," she said, "and then I get out of the water and look into the mirror and I can't believe the old woman staring back is me!"

One lunchtime late in the week I paid a taxi driver to give me a city tour, and he took me to the smelly tannery, along the pink-tinged ramparts and to delve into the souks. I was hungry to experience more, but this was a holiday with swimming at its heart, and time was running out.

Everyone else had made great strides but I was still floundering when I attempted breaststroke. For the final two sessions, Steven showed me front crawl. Within two strokes I put my foot down again, but for those precious few seconds I was swimming and, for once, enjoying the sensation of being in the water. In seven days I had made more progress in the water than in the past 30 years, and I was determined to build on what Steven had taught me.

• The next Art of Swimming (0845 604 1910, artofswimming.com) holiday in Marrakech with Steven Shaw departs on 8 May and costs from £1,600pp (single room) including flights, lessons and seven nights' B&B at the Kenzi Farah Hotel. A three-day course in Ashby-de-la-Zouch, Leics, runs from 24 February and costs £530pp for a single room