"Let me tell you about the magic dolphins,” Manuel, our ever-smiling guide, says, as we travel overland from Iquitos, the gateway to the world’s biggest (if not longest) river, to Nauta, about 60 miles downstream.

It is here we shall meet our home for the next few days, the good ship M/V Aqua, the first luxury vessel to tour the Peruvian Amazon.

I’ve been tempted by promises of 230 sq ft cabins, four-course feasts, air-conditioned everything and a pisco sour before bed – not to mention some of the world’s most spectacular wildlife just outside my room’s 15ft panoramic window. But that’s for later. Did you say magic dolphins?

“The locals believe the dolphins come out of the water and turn into humans, who then walk into villages looking for only the most beautiful men and women,” explains Manuel, who at 25 is already deeply versed in the language of the jungle. “They bring them down to the riverbank to make love, but then drag them into the water, turn them into dolphins and live with them for ever.”

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He laughs at this dose of Amazon irrationality, but then turns back, suddenly serious: “So no flirting with the dolphins.”

It’s no good. Despite such grave warnings, I can’t help it. In fact, looking back, not only must I confess to considerable coquettishness with every pink river dolphin that played hide-and-seek with our boat, but I’m afraid I couldn’t even limit myself to amorous mammals.

I was – I admit it – a tart to the entire rainforest. I purred in front of parrots, especially the hilarious festive parrots who attract a mate by ducking and dancing from side to side like singers on MTV Base. I swooned at three-toed sloths, clamoured over capuchin monkeys, bowed to the black-collared hawk with its iridescent green wing feathers and steely gaze, and raised a quizzical eyebrow at a dusky titi monkey. And what I did in front of a pair of wattled jacanas doesn’t bear repeating in a family newspaper.

THERE ARE a number of ways to explore the Amazon, depending on what you’re after, what you can afford and what you can handle. Excursions by canoe, speedboat and cruiser are available, as are stays in lodges and camps with varying levels of amenities.

The Aqua takes the hardship and discomfort often associated with those options and gets its butler to dispose of them discreetly. It can accommodate up to 24 passengers alongside its 19 staff, which includes two chefs, a pastry cook, three outstanding guides and a paramedic.

The food, overseen by the celebrated Peruvian chef Pedro Miguel Schiaffino and cooked entirely on board, is extraordinary. For dinner you might start with baked scallops with parmesan cheese and pisco, progress through freshwater shrimp with saffron rice and finish off with baked pears in red wine and spices, while the house band play local, and not so local, medleys on traditional instruments.

Yet, for all its decadence, there is a genuine USP to the Aqua beyond that of mere comfort. Being a craft of considerable heft – it’s 130ft long and weighs 180 tons – it is able to conquer currents, debris and distance without difficulty, meaning that it can travel further up the river, and more quickly, than pretty much any other vessel in its class. And the advantage of this? Once we had left the port of Nauta behind, I didn’t see a single tourist beyond those on our ship. The Amazon was ours.

The boat has three skiffs that seat 10, including a guide, and it is aboard these that the love affair begins. Their four-stroke engines slide you along the still waters almost silently, which means you can get up close and personal with whatever appears round the next bend – close enough to look a dolphin, a kingfisher or a tarantula straight in the eye, and then hand it your phone number.

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