We awoke to screams. It was the children flinging themselves lemming-like into the bracing waters of an eastern Mediterranean dawn. Deep water and kids is usually a combination designed to spring us parents – the sort to issue armbands at bath time – from our cabin bunks, gibbering “Man overboard” and going for the ship’s klaxon. What was it about life on board a Turkish gulet that had us smiling to ourselves and slipping back into sea-rocked slumbers?

Except for cross-Channel ferries, canal boats, ocean liners and pedalos on the Serpentine, most parents don’t much trust their youngsters on things that float. Yet here were three couples taking their kids to sea for a week; when the combined brood numbered an unruly eight, aged from 3 to 10; and when the youngest in each family couldn’t even swim.

Enter the gulet, the signature craft of southwest Turkey. Forget the flotilla yachts that also frequent the sheltered waters between Bodrum and Antalya; it is the romantic timbered lines of the gulet that is the defining summer craft along this mazy, mountain-backed coastline, home to the fire-breathing chimera and to St Nicholas, to ancient oracles and Byzantine hermits. Originally built to ship mandarins and lemons, the anchor-anywhere gulet has since built a devoted following among fair-weather yachting types, discerning indolents and people looking to improve on the package-resort experience.

Mix informal measures of the above on spacious decks and at generous alfresco dining tables, along a coast brimming with hidden coves, bays, ruin-strewn islets and beaches and you’ve one of the best – and best-value – barefoot luxury holidays ever invented. Even for children.

“Cafreful!” yelled several anxious parents as the children swarmed up the Randa’s gangplank. “Cool!” replied the children as they took possession of their holiday home to discover how shamelessly spacious these vessels have become in the course of their conversion from freight to pleasure. Randa’s widened waist accommodated eight wood-panelled double cabins with ensuite bathrooms. The main cabin-galley backed onto an extended stern deck, the outdoor living and dining area, with an apparent acreage of cabin roof given over to sun mattresses. A windsurfer, canoe and snorkelling gear, hot showers, music system, board games, a chest-sized cold box for drinks, and fully staffed service meant we were as long on facilities as we were on space.

Which left the biggest of issues: safety. Captain Tuncay’s detailed drill – the whereabouts of life jackets, no running on board, swimming only with permission, children to stay on the rear deck when the Randa was on the move – soon had parental fears subsiding. There was more good news in the solid wooden bulwarks that rose from the boat’s sides to the shoulders of the nonswimmers, three-year-old Esme and four-year-old Lizzie and Zak.

Barely half an hour had passed before the holiday had settled into its established pattern: the Randa anchored in a deserted cove, the calm sea turning choppy with happy, flailing children, and the parents being fixed drinks under a flaring sunset as Cetin, the cook, set about the first of many excellent Turkish meals.

In the morning, ballasted by a breakfast of eggs and olives, oil-drizzled cheeses, tomatoes, melons and cherries, rosehip and apricot jams, we sailed east. We had chosen as our cruising grounds the stretch of coast from Dalyan to Fethiye Bay. Here were several anchorages. Short hops, never longer than three hours, kept the seasickness to a minimum and brought us to new stops by lunchtime. We moored in the sheltered bays of our choice: Aglimani, Boynuzbuku and among the waterside ruins at Hamam Bay, where an old houseboat abloom with geraniums potted in rusting olive-oil tins served as a ramshackle teahouse. At Gemiler we snorkelled over starfish and ancient stone cisterns before putting ashore on to explore an overgrown monastic settlement dating from the early Byzantines. The adults sought out mosaics and fresco fragments among the 5th-century basilicas while the kids searched for lizards, crickets and tortoises. And kept an eye out for the ice-cream boat.

Then there was the Dalyan River, where the Randa could not go, but with enough attractions – wildlife, ruins, swimming lakes and beaches, and even a smelly sulphur mud bath for face decorating – to be tailor-made for the children. A local caïque picked us up from our anchorage after breakfast and ferried us up the twisting, turtle-dotted river to the ruins at Caunos. It was perhaps too much to expect that the children should appreciate the history of this beguiling city, with its hilltop citadel and long-silted harbour, but the girls recognised a stage when they saw the theatre, putting German visitors to flight and setting a stray dog howling with a rousing rendition of a Girls Aloud number.

Late in the afternoon we stopped at Iztuzu, one of the Mediterranean’s most panoramically unspoilt beaches, to swim in the surf and wash off the mud masks – cats, pirates, Father Christmas beards – the kids had adorned us with at the thermal mud bath. Six-year-old Olly pronounced it his best day ever.

As for trouble, well, the nearest thing to it was when Olly trod on a sea urchin while snorkelling. He was brave about it, especially when the crew told him that a little olive oil, applied every morning, would soften the skin and soon bring the spines to the surface. The spines came home with him – along with the rest of us, intact and perfectly enchanted.

• Jeremy Seal and family were guests of Tussock Cruising and Pure Holidays

Travel details: Tussock Cruising (020 8510 9292, www.tussockcruising.com) offers the 16-berth Randa from £2,750 to £4,380 per week (for the whole boat), plus £203 per adult (£101 per child) to cover food and all drinks. Or try Blue Cruise (020 8968 7770, www.bluecruise.co.uk), which has six- to eight-cabin vessels from £399pp, including all meals on board and transfers. Neither company includes flights.

Other companies offering private gulet charters include Westminster Classic Tours (020 8286 7842, www.wct99.com), DayDreams (020 7637 8921, www.turkishcruises.co.uk), and Simpson (0845 811 6506, www.simpsontravel.com). Charter flights operate to Dalaman from 22 UK airports, and Dublin. Pure Holidays (0870 777 0737, www.pureholidays.com) has flights from £134 return during October. Or try Charter Flight Centre (0845 045 0153, www.charterflights.co.uk).

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