WHEN my daughter May, 4, came running up with a piece of 3,500-year-old Mycenaean pottery, my heart sank. She and her sister Sorrel, 8, had been grubbing around in the mud next to a dig at Midea in the Peloponnese and uncovered pot shards overlooked by the excavators.

In Greece, if you’re suspected of treasure-hunting on sites, an arrest is almost certain. So the treasure had to be wrested from her hands and a swift departure made.

We had come to this part of Greece because I was writing a book and preparing a TV programme about Helen of Troy, the original sex goddess whose beauty was said to have sparked the Trojan War. While everyone remembers Helen as the face that launched a thousand ships, few recall how many miles she clocked up in her various erotic liaisons. Greece, Turkey, Libya, Lebanon, Egypt, Cyprus, Crete — as well as seeing it all, she saw them all. So when I set out to write about Helen’s roots in prehistory — and to identify the traces she has left in Western civilisation — I knew that for at least part of the gargantuan journey the family would have to come along too.

Replicating Helen’s journeys where possible, we started with a boat trip from Cape Sounion, south of Athens, to the Peloponnese. As a start to our adventure the boat trip could not have been more magical. Children fractious from a long flight were lulled by the hum of the SeaCat. The water was a looking-glass — broken only when we were paced by dolphins. I mused that with sea travel so much a part of Greek life, Helen must also have taken such journeys.

In search of a bed for the night we hopped off at the island of Aegina (where gold artefacts from the Late Bronze Age — the period in which Helen lived — have been found), and when that drew a blank, the island of Kythera (medieval versions of the story insist that the Trojan prince Paris first espied Helen worshipping at the temple of Aphrodite here). All rooms alongside both quaysides were full — a reminder that at the end of October when the sun is still golden, Greeks flock to the resorts normally populated by tourists.

So we backtracked and landed at Hydra — a good move. Staying in a converted sponge factory called Bratsera with one of the few swimming pools on the island (water is at a premium here), we found a romantic hideaway that I imagined Helen would relish with lemons, jasmine and geraniums in the courtyard and homemade marmalade for breakfast.

Later, we visited the Argolid plain — the centre of Greek power in the Late Bronze Age and the home of impressive Mycenaean sites. All of them, Mycenae itself, Tiryns, Midea and Argos, had a reputation for fostering skilled horse- riders — in the Iliad, Agamemnon the King of Mycenae is “that skilled breaker of horses”. Little has changed. The equine tradition still has verve. Today the city of Argos itself is a workaday place, jaunty but a bit rough-neck. As we passed through we found ourselves in the middle of a horse carnival: lusty-looking men clattered down the streets, playing dodge with the cars. There had been a race between neighbouring towns: you could virtually smell the testosterone in the air.

And then suddenly — a gypsy boy appeared. Like the other men he wore no hard hat, but unlike them he was bare-chested. The horse was saddleless and around its neck swung a bright necklace — two strings of turquoise and coral beads, at the bottom a leather pendant in the shape of a heart. Immediately I had in mind those ancient heroes of Greece who, we are told, thundered through Greece to try to win Helen’s hand in a marriage contest; hot and brown, a lot of flesh on show, all yearning to win glory and a princess. I told my girls the stories as we drove out of Argos and on to Mycenae itself — the gypsy boy, grinning, clattered behind us.

We also stayed at La Belle Helene, a guest house just south of Mycenae. It was the base for the archaeologist Heinrich Schliemann when he excavated Mycenae and has attracted an astonishing array of visitors: Virginia Woolf, Benjamin Britten, Jean-Paul Sartre, Heinrich Himmler — all of whom signed the visitors’ book.

I went back there while shooting my documentary about Helen for Channel 4 and woke up covered in mosquito bites — one on the end of my nose swelled up to the size of a small ping-pong ball. But the view of the mountains from Herr Schliemann’s old room can’t be beaten.

The citadel of Mycenae itself can never disappoint. Cradled by the Arachnaion mountain range, it is all you could hope for in a ruin — secret underground water cisterns to explore by torchlight, worn marble walkways and gasp-making artistry. Here you can see the golden Mask of Agamemnon, finely wrought bronze swords and grotesque figurines.

As we watched the sun go down from the throne room, and imagined these treasures on show in the Bronze Age palace, it was clear that my two girls thought this was a journey worth making.

Times recommends

• Confessions at 39,000 feet - your stories
• Europe's 20 best Christmas markets 2009
• Cruise passengers say: ‘We’ll tip when we want to’