"Ok everyone, swim for it!" our skipper Robert says with a grin as the engine of our boat shudders to a halt, the greenery of Kakadu National Park to our left and the golden escarpments of Arnhem Land to the right. I know he's only kidding, but I can't help but glance nervously into the murky depths of the East Alligator River. Not a chance. 

Here, numbers of the once endangered saltwater crocodile, known as ginga by the local Bininj and Mungguy people, have rebounded to healthy levels, making them one of the region's greatest tourist lures. 

Just as the East Alligator River has been misleadingly named, when explorer Phillip Parker King in 1820 mistook the crocs for the alligators that he had encountered in the Americas, so too have the saltwater crocs. For, while smaller freshwater crocodiles are true to their name, salties can live in both fresh and saltwater environments.

We spot our first croc of the day on the riverbank as the engine of the Guluyambi Cruises boat purrs its way back to life. She's a big beast, all four metres of her scaly flesh curled around the trunk of a paperbark tree.

We glide past her slowly, but a long dark shape drifting alongside us suddenly diverts our attention. I might have mistaken it for a stick if it wasn't for the two eyes stealthily peering just above the surface of the opaque water. They fix on us for one electrifying second before they sink out of sight.

We watch for the bubbles to reemerge, but movement on the approaching sand bar steals our interest away once again. Two crocs are baking in the sun, close to the spot where Robert tells us scenes from the 1986 classic Crocodile Dundee were filmed.

But while this waterway is famous for its crocs, they aren't the only predators in this river, he adds. In fact, the baby crocodiles often fall prey to reef and bull sharks that lurk in the depths. I sit a little firmer in my seat.

The next day, however, we do go for a dip. It's much needed too after a sticky morning exploring rock art in 38 degree heat at Narlangie Rock, one of more than 5000 art sites in Kakadu where rust red markings record thousands of years of changes in the landscape and the Aboriginal way of life.

As our Intrepid truck pulls in at the entrance to Barramundi Gorge, we spot a sign clearly marked with a crocodile and a single word: Warning.

"So, there are no crocodiles in here?" I ask anxiously. "No salties," our tour leader Paul promises. Each year, at the end of the wet season, the park rangers trawl the region's swimming holes for crocodiles that have moved in during the rains, relocating them to areas out of harm's way. 

He points out a long cage in the water, half hidden between the pandanus fronds spilling over into the creek. It's a crocodile trap – deployed just in case any saltwater crocs creep back in during the dry season.

There are probably a few freshwater crocs in the vicinity, he admits, but they're far smaller and are more interested in small prey such as insects, frogs and little fish than humans.

I'm feeling a little more reassured by the time the short hike brings us out at the base of a waterfall. Now coated in sweat and hot dust and with temperatures hitting 41 degrees, cooling down is foremost in my mind.

Clear water cascades over the rocks into a plunge pool fringed by palms. Remove the handful of tourists and the scene provides a glimpse of Australia before the arrival of balanda (non-Aboriginal people) – wild and unspoilt. 
We brace ourselves as we gingerly pierce the water toe by toe, but there's no need – the glassy green pool is tepid as bath water. I swim over to the mossy rocks beneath the cascade and get splattered by the torrent of refreshing water. Not a croc in sight.

Now, I just need to taste crocodile. And luckily for me, it's on the evening's menu.

After cooling down in the pool at the Springvale Homestead, where we are camping in tented huts, we gather in the Intrepid kitchen for dinner. More than just our tour leader, Paul is also our chef. He plonks a huge platter of marinated kangaroo and citrus soaked crocodile in front of us.

"Dig in," he instructs. We tuck into the mound of kangaroo immediately – we're all familiar with its gamey taste. But we're a little more hesitant when it comes to the croc.

"It tastes like chicken right?" I ask. Isn't everything supposed to, after all? "It's a farmed croc, so it'll either taste of chicken or fish, depending on what it's been fed," Paul explains.

Definitely fish, I think as I eat some. These creatures are both fascinating and terrifying, but above all, they're chewy.

The writer visited Kakadu National Park courtesy of Intrepid Travel