I am holding on hard to the 112-year-old Bessie Ellen. We are in a force eight gale off the Hebrides. I am wearing every piece of clothing that I possess under my oilskins and I’m still cold. But that doesn’t matter. What does matter is that I continue to hold on to this rope.

There is a pause before frantic activity. Into that pause comes stinging hail. My hands are numb. Then someone shouts “Run!” and I’m running with the rope as fast as I can. Only that’s not fast enough. The Bessie Ellen is pitching in the high seas, so I am running uphill on wet wooden boards. Like a cartoon character, I’m going nowhere.

One of the ship’s crew sees my predicament, reaches for the rope and, with younger legs, runs for me. The Bessie Ellen turns and fairly whips through the grey-white waters of north-west Scotland.

The Bessie Ellen is Britain’s last remaining ketch – a wooden sailing ship of the kind that once transported cargo around the west of England – still under sail, and we are whizzing past the rain-masked coasts of the Hebrides at an exhilarating top speed of 8.4 knots (about 10mph). Around me the rest of our 18-strong crew are recovering from our jibe in high winds (that’s changing direction to you and me); I joke with one of my fellow passengers, Eve Hallam, a 33-year-old paediatric intensive care nurse, that my gloves turned white with the hail. “What hail?” she asks, and laughs, realising she hadn’t noticed the weather.

I’ve never sailed before, but if this is sailing, then I’m addicted. So, it seems, is everyone else: 85% of the Bessie Ellen’s guests return for further sailing adventures.

The story began in Plymouth in 1904 with a shipbuilder called William Kelly. Times were hard in the shipyard at that point and rather than lay his men off, he built the Bessie Ellen to keep them employed.

For 41 years the ship sailed round Britain’s western coasts and Ireland delivering cargo. Its first shipment was 150 tonnes of manure from Plymouth to Bideford; but during the Second World War it also carried pit props, hops, salt and ultimately a hull full of tinned fruit and white flour to American service personnel based in the UK. In 1947 it was bought by a Dane, and ran cargoes around Denmark until the 1970s. Sailing on it is a real-life history lesson and – as there is no phone signal – a chance to get away from modern life.

“Having a finger on our past is important,” says the Bessie Ellen’s skipper and owner, Nikki Alford. “The ship is a moving part of our heritage.”

I’m sailing for four days round the Hebrides. We call in for half an hour at Tobermory on the Isle of Mull. The rest of the time we are at sea. Dolphins swim alongside our prow one evening. Inquisitive seals pop up and check us out. Puffins, oystercatchers, fulmars and shags get on with their lives around us.

A bond quickly forms between the 12 guests and six crew. As guests, we are living in the former cargo hull, eating sumptuous meals prepared by chef Peter Thompson in a tiny galley. The smell of the next meal wafts through into our living space. Will tonight be nettle risotto, or Moroccan fish stew? We sleep in small bunks along the Bessie Ellen’s sides, our modesty protected by flowery curtains that Nikki made. You can reach out and touch the original wooden boards put in place by Devon craftsmen more than 100 years ago.

Fortunately there are no night watches for the guests, only the crew. We are woken in the morning by the thin light of a Scottish dawn filtering through the portholes and Peter heading to the kitchen to make tea, porridge and bread. Meals are hugely convivial. Having exhausted ourselves pulling ropes, hoisting the mainsail (which requires effort from everyone) and keeping the Bessie Ellen shipshape, we are ravenously hungry.

On our way towards Lunga – an island famed for its puffins – Eve and I are given charge of the ship and allowed to steer. “Just keep the headland between the prow and the rigging,” says Nikki, and wanders off. At first, being at the helm is unnerving, then magical. Some people refuse meals and remain on deck just for the sheer pleasure of sailing the ship.

First to volunteer to climb the rigging is 74-year-old Arthur Winterburn, a former builder. He’s been brought along by his nephew, Doug, as his wife of 48 years, Sylvia, has recently died.

Elin Dieme, from Graham Island off the coast of British Columbia, is the youngest person aboard. Having grown up on an island with just over 3,000 people and one road, she felt the need to see the world. “I had my 18th birthday, sat my last exam and flew out here,” she says. “It’s been amazing.”

On our last night we weigh anchor just off the island of Kerrera. Highland cattle and hardy sheep are grazing. There isn’t a soul in sight. Over a dram of whisky everyone agrees that turning the Bessie Ellen around in a force eight gale was the highlight of the trip.

“Where are you going next?” I ask Nikki. “The Arctic,” she says. “Want to come?”

• Berths are available for seven-day trips from Douarnenez, Brittany to Newlyn (departing 23 July, £750), Newlyn to Oban (30 July, £690) and Oban to Aalborg in Denmark (3 September, £850). For more information, go to bessie-ellen.com