A black-tipped shark, some five feet long, circled the ship as we gathered on deck for lifeboat drill. “Don’t worry, he’s had lunch,” joked one of the officers on Celebrity Cruises‘ Xperience, my floating home for the week.

The shark certainly wasn’t interested in a large green turtle that popped its head out of the water, or the snaking form of a marine iguana swimming for shore. I, on the other hand, was hopping with excitement. All this, and we hadn’t even set sail.

The Galapagos archipelago, straddling the equator 600 miles off the coast of Ecuador, had already captivated me. Of course, blue-footed boobies and prehistoric-looking lizards are familiar characters, thanks to David Attenborough, but from the minute I almost tripped over a land iguana basking outside Baltra airport, I was enchanted.

We plunged straight in later that day with our first hike, on North Seymour island, over black, spiky lava on which pterodactyl-like frigate birds were puffing out their scarlet pouches in courtship displays.

Sea lions flopped fatly on the sparkly black beach, hoiking themselves in and out of the water, big-eyed pups nestling next to their mothers. The animals are completely unafraid, so much so that a German tourist was able to capture four land iguanas in 2012 to smuggle home. He was apprehended at the airport and sentenced to four years.

I quickly discovered that a week in the Galapagos is no beach break. You’re up early for breakfast, then ashore to hike or snorkel, grabbing a siesta as the ship sails to a new anchorage, then ashore again, wildlife lecture, dinner, drinks and bed. You need a degree of fitness and stamina.

All 19 islands of the Galapagos are volcanic but they’ve formed over millions of years so all look different. We explored high cliffs, sea caves, tumbled rocks and jagged lava fields. Some islands are dessicated, studded with candelabra cacti, while others are covered with frankincense trees. Beaches come in shades of green, when there’s olivine in the rock, or icing sugar white, turtle tracks running up from the water to buried nests.

On San Cristobal, we clambered through a hollowed-out stream bed, pushing our way through spiky green shrubs to a high, rocky plateau and an extraordinary sight: thousands of blue-footed boobies honking and hopping from one foot to the other in hopeful courting displays. One female coolly preened her feathers as three suitors simultaneously strutted their stuff.

While I loved the hikes, the underwater world was the real lure. In the aquamarine depths off Floreana, graceful sea turtles glided just underneath me. From Punta Moreno on Isabela island, shoals of yellow and purple angelfish shimmied along a rock wall, two sea lions frolicking round me like puppies. I gasped as a shark cruised underneath me – but it had other business, as did the flock of penguins I inadvertently interrupted; they bobbed around my head for a bit as I surfaced and zoomed off under the water like bullets, to fish. In the cold, deep water off Española, black rocks on the sea floor were pointed like witches’ hats, while buried stingrays would shake themselves off and dart across the sand.

We only called once into ‘civilisation’, the tiny port of Puerto Ayora. Even here, wildlife is everywhere.

Animals take priority over humans everywhere. You always have to stick to the trails out on the islands and you’re not allowed to walk within three metres of anything — although sometimes, it’s difficult.

Evenings on board were lively affairs as 42 of us, from Canada, the USA, Britain, Australia and Chile, swapped stories over colourful Ecuadorian dishes – curried quinoa, spicy ceviche, plantain chips and fresh snapper in coconut sauce, washed down with Chilean and Argentinean wines, all of which were included in the price. One night, we anchored off San Cristobal for a deck barbecue and a blazing sunset that threw Kicker Rock, a sheer, 460-foot volcanic spike rising out of the sea, into dramatic silhouette.

I confess to sniffling behind my sunglasses (and I certainly wasn’t the only one) as we skimmed across the water on the Zodiac to the dock in Baltra for the journey home. The Galapagos is an extraordinary, life-affirming place. I’d challenge anybody not to be profoundly moved by it.