I am standing in a hot, dusty town centre filled with low-slung, Soviet-outpost-style architecture. The main square is dominated by a large, brightly painted statue of Santa Claus on a plinth, around which two of my children are riding camels. It is the kind of image one might offer as evidence that dreams make no sense, but it's not a dream. I am actually here, and this is actually happening.

This is the town of Demre in southern Turkey, home of the Church of St Nicholas, though it is neither the man's birthplace nor his final resting place. He was born in Patara, just up the coast, and though he was originally entombed in the church, his bones were stolen by Italian sailors in 1087 and taken to Bari. Demre is, however, a sort of official anti-Lapland; the place where you take your kids to cure them of their belief in Santa Claus.

We have been bussed here unexpectedly as compensation for a boat trip that was cut short by rough seas. We have already seen the ruins of ancient Myra, where Santa tat fills the stalls lining the entrance. The children in our party have been told that Saint Nicholas, the real Santa Claus, was from around these parts, but none of them thought to ask how a fourth-century Lycian bishop managed to migrate north and train up some flying reindeer for the purpose of distributing toys across the globe every Christmas Eve for the past 600-odd years.

In Demre, however, the anomalies are so blatant as to be beyond question. St Nicholas was buried here, which means Santa Claus is dead. For any child able to ride around a Santa statue on a camel with their faith still intact, there is a helpfully disabusing explanatory plaque in the museum. It describes, in slightly weird English, how a traditional northern European myth has been conflated with the legend of a genuine saint, creating a "very popular half-religious character" who rides in a sleigh pulled by reindeer. "In fact," it goes on to say, "the places where the real Nicholas lived are on the coast of the Mediterranean where it has never snowed... Though it is against reality, Father Christmas lives as a charming personality for whom children wait in almost all Christian countries." In other words, kids, there ain't no Santy Claus.

I can't help finding this a little hypocritical, given that almost everything we know about the historical St Nicholas is probably untrue. It is said that as a baby he was so devout that he abstained from his mother's breast on canonical fasting days. It is alleged that he once resurrected three children who had been pickled in brine by an evil butcher, though it is against reality. Another version of this tale has three clerks being turned into meat pies, said to be the legend on which Sweeney Todd is based, but there isn't a plaque in the museum telling Sondheim lovers that there is no Sweeney Todd.

Fortunately, my children show absolutely no interest in the museum, preferring to spend the allotted 45 minutes looking in shops. If the younger ones find any of this troublesome, they don't say anything. In the past whenever evidence challenging the existence of Father Christmas emerged, my children would construct their own elaborate explanations as to how he could enter homes without chimneys, or manufacture Nintendo products under licence. Maybe they don't care any more, I think. Or maybe it's just too hot.

The issue finally arises on the bus, when the children overhear the adults discussing it, and we fall into an immediate and wholly transparent silence. "Oh, come on, Dad," says the youngest. "It's not like I didn't actually see you last time creeping into my room and putting my stocking on my bed."

He has never told me this before. I am monstrously disappointed.

"It wasn't me," I say feebly. "That wasn't me."