Marlon Brando's blue lagoon in the Cook Islands

Our skipper Kimi points towards the ‘runway’, and it takes a moment or two to realise what he means. The flights that landed at Akaiami were a bit special. 

Between 1951 and 1960, Tasman Empire Airlines Ltd (TEAL) would drop the likes of John Wayne and Marlon Brando off here for a few hours while the plane refuelled on the way to Tahiti.

But there’s no tarmac in sight. The TEAL planes were flying boats, the Orient-Express of the air back in the day, and they landed on the clear, sparkling waters of what must be the most staggering lagoon on Earth.

A tour boat calls at One Foot Island in Akaiami, one of the 15 islets in the Aitutaki atoll of the Cook Islands in the Pacific Ocean

A tour boat calls at One Foot Island in Akaiami, one of the 15 islets in the Aitutaki atoll of the Cook Islands in the Pacific Ocean

Marlon Brandon was a regular visitor to Akaiami when travelling to Tahiti to film Mutiny on the Bounty 

Marlon Brandon was a regular visitor to Akaiami when travelling to Tahiti to film Mutiny on the Bounty 

Akaiami is one of the 15 islets in the Aitutaki atoll of the Cook Islands in the Pacific Ocean. There may be green hills covered in banana plants and starfruit trees inland, but Aitutaki is dominated by its lagoon. 

On a dull day it is a vision of majestic light blues, fringed by a reef and several islets playing to the tropical coconut palm stereotype. But as soon as the sun comes out… oh boy.

The beaches are of the dreamiest white sand, and the water sparkles in teals, turquoises and milky translucence. Any happy snap taken here is sure to fire the envy factor up to 11 for anyone looking at it back home.

Kimi has the not-too-arduous task of keeping everyone entertained as the Bishop’s Cruises boat glides along Aitutaki’s lagoon, stopping off at some of those islets. 

This sometimes involves husking a coconut, and at other times demonstrating a zillion ways to wear a pareu – the local equivalent of a sarong. But mostly it’s a case of letting the lagoon do the talking.

Akaiami is the first stop, and there’s a little bit of information about its strange aviation history. But most aren’t too bothered about reading signs – there’s some of the most beautiful water on the planet to splash in.

The boat then moves on to One Foot Island, at the far end of the lagoon. Snorkels are donned as Kimi and his team barbecue tuna caught fresh that morning by the skipper.

It doesn’t take long nosying at what lies beneath the water’s surface to find some giant clams. Angelfish flit around them, and shoals of goatfish – with their distinctive yellow stripes livening up a pallid body – whoosh past.

David's tour also took in One Foot Island - another heavenly spot in the Cook Islands

David's tour also took in One Foot Island - another heavenly spot in the Cook Islands

At One Foot Island, pictured, David eats barbecued tuna that was caught just hours previously

At One Foot Island, pictured, David eats barbecued tuna that was caught just hours previously

TEAL flying boats, pictured, refuelled in Akaiami en route to Tahiti during the 50s and 60s

TEAL flying boats, pictured, refuelled in Akaiami en route to Tahiti during the 50s and 60s

But the real action, it seems, is next to the boat. A yelp comes up from a woman in the water. She has been startled by an absolute monster of a fish.

The giant trevally grow, well, giant here – and they’re not shy. Three of them are zooming around at alarming pace, occasionally leaping up to the surface.

They have quite a territory here, and they don’t seem to mind sharing it with humans ticking off a true bucket-list treasure.

TRAVEL FACTS 

Air New Zealand (airnewzealand.co.uk) flies from Heathrow to Rarotonga via Los Angeles. Return fares cost from £1,307. From there, Air Rarotonga (airraro.com) flights to Aitutaki cost from about £276. 

The Tamanu Beach Resort (tamanubeach.com) offers coconut palm-thatched bungalows, a stretch of beach, and free kayaks and snorkel gear to explore the lagoon. Prices start from £281 per room. The Bishop’s Cruise (bishopscruises.com) on the Aitutaki Lagoon costs about £54. More information: cookislands.travel