“ARE these real Roman columns, Daddy,” my eight-year-old daughter, Ella, asks as we climb over a submerged Doric column in the crystal-clear mineral waters below us and wade into deeper waters.

“I don’t think so,” I tell her. They’re probably replicas, and the real ones might be in the museum.

“They look real,” Ella tells me.

I spend the next hour dividing my time between watching the kids swimming beneath the luxuriously warm waters - where Cleopatra and Mark Anthony also bathed two millennia ago - and wondering if those columns are real or not. They certainly look and feel like marble, and the pool is called the Antique Pool as well as Cleopatra’s Pool.

Once we dry off and we’ve found our guide it’s the first question I ask her. “Of course, they’re real,” she replies. They were part of a temple to the god Apollo and used to hold up a roof, but the roof was destroyed many centuries ago.”

I’m not sure why I ever doubted this, Turkey is teeming with ancient cities and artifacts after all. Perhaps it’s because there is something so other worldly about Pamukkale and Hierapolis - where the pools are situated - that it’s hard to know if you’re dreaming or not at times.

Just around the corner from Cleopatra’s Pool are the most surreal pools I have ever visited in my life, and that includes the legendary Blue Lagoon in Iceland. The terraces of Pamukkale - which is Turkish for “cotton castle” are a dreamlike landscape, of mineral forests, petrified waterfalls and terraces with warm water pools that would impress even the most jaded of travellers. It looks, for all the world like an ice palace and can be seen from many miles away. There are only two places like this in the entire world, with the other, in Tuscany, being far smaller and not having the ruins of an ancient city next door.

We spend another hour on these unreal terraces wading through the various thermal pools and playing with the white silt on the bottom, or watching fellow tourists making strange poses next to the calcite stalactites or sitting in a shallow river of thermal waters, which our kids mistake for a waterslide. Everywhere there is white, and sunlight reflects from it in strange ways, washing out colours as it does so. Then it’s time to move on and explore some of the ancient city of Hierapolis, which is around a 10-minute walk away from the terraces.

Most package tourists who holiday in the Turkish resort of Kusadasi - where we are based - visit the ancient city of Ephesus, and for good reason. It’s the best preserved and most impressive example of a Greco-Roman city in the world, with only Pompei giving it a run for its money. Plus, it’s exceptionally close to the resort of Kusadasi. But only a fraction of those visitors venture as far away as Hierapolis and Pamukkale, which are two and a half hours from Kusadasi by road. For me, Pamukkale and Hierapolis are even more impressive than Ephesus, and the 12,000-seater Roman amphitheatre that sits just above Cleopatra’s Pool is the icing on the cake.

When we arrive at the amphitheatre, there are only around 12 other people besides us. In contrast, the ruins of Ephesus felt like a rugby scrum at times, thanks to thousands of tourists arriving on multiple cruise ships that day. Admittedly, the amphitheatre at Ephesus is more impressive - it holds 25,000 people and still hosts performances today - but Hierapolis amphitheatre is impressive nonetheless, with spectacular views of the valleys below; as well as the other ruins of the site.

Our day trip ends with a late lunch and another swim in thermal pools at a nearby hotel, this time with orange/brown stalactites from the mineral deposits as our backdrop. Then we head back to our hotel in Kusadasi. It will take another two and a half hours to get back to our hotel and by the time we return the onsite waterpark - a common feature at resorts in Kusadasi - will be closed. The kids aren’t happy when they realise this, as they’ve been hurtling down the slides non stop for the last few days, but I remind them that they’ve been in three pools unlike any in the world today and they nod in acknowledgement before settling down on the coach. They’re already looking forward to 10am the following day, when they can frolic to their hearts content in more modern surroundings again.

Kusadasi is a popular resort on the Aegean, with dozens of high quality resorts. All inclusive resorts are particularly popular, some of which are more geared to adults and others to families. We stayed at the Palm Wings Ephesus, which had three large swimming areas - including an adults-only pool and a fantastic waterpark. There was also a first-class beach and water sports centre, seven bars and beautifully manicured gardens with roaming peacocks. One week all inclusive at the Palm Wings Ephesus can be found at TUI for £586pp in October or £623 at half-term.

Trips to Pamukkale are best booked via TUI and are well worth the £84pp, as they include travel, entry to the ancient city of Hierapolis, a swim in Cleopatra’s Pool, entrance to the “cotton castle” terraces and dinner, swim and entrance to thermal pools in a five-star hotel. Ephesus can easily be visited independently by taxi from the Palm Wings Ephesus or booked via an excursion with TUI or local operators if staying further afield.