Viewers following the advance of the HMS Endeavour towards these shores via Foxtel’s new series The Pacific: In the Wake of Captain Cook, have over the past fortnight enjoyed an unexpectedly fresh take on the young Yorkshire lieutenant’s first voyage of discovery. Did we really need a six-part, in-depth exploration of Captain Cook? Of course not. But fortunately, The Pacific isn’t much interested in setting the usual hoary course. Instead, with the rakish Sam Neill at the helm, the series provides an alternative rendering to the usual glorification of empire, and the result is surprisingly enjoyable.

The first two episodes, on Cook and his reeking ships’ company in Tahiti and New Zealand, often centre on the experiences of the pre-existing indigenous nations during their various interactions with the British expedition. Neill traces Cook’s journey himself, crossing the Pacific Ocean to the places Cook visited and to speak to people along the way. The unfamiliar approach enables different, far more engaging stories to be told.

It also throws new light on eminent characters – such as the naturalist Joseph Banks, who accompanied Cook on his voyage – as well as historical figures who played key roles in many of the voyage’s feats but who have since had their contributions largely downplayed. The show’s focus on the lesser-celebrated contributions of Polynesian polymath Tupaea to the expedition’s accomplishments in navigation and diplomacy – triumphs generally attributed solely to the likes of Cook and Banks – is an example of the kind of welcome shifts in perspective that are becoming increasingly important to contemporary nations such as Australia in reconciling the heavy burdens of their colonial past.

‘The focus on the lesser-celebrated contributions of Polynesian polymath Tupaea is a … welcome shift in perspective.’ Photograph: Foxtel

Monday’s episode, the season’s third, sees the expedition hop the ditch from Aotearoa, aspiring to locate the mythical southern continent of Terra Australis. Instead, the voyage chances upon the previously uncharted east coast of a landmass known as New Holland. But as Cook makes his way north, sailing just off the continent’s coastline, the Endeavour’s progress is being monitored closely by a collaborative border force of wary locals.

The customary narrative of Cook’s arrival here is a divisive one. At one end of the cultural spectrum sits the likes of Australia’s current prime minister, who seeks to erect a $3m aquatic effigy to James Cook in Botany Bay, just off the shoreline of modern-day Kurnell, where the navigator and explorer’s landing party first intruded on Gweagle lands on 29 April 1770. At the other end of the spectrum you will discover people like me, who consider the Australian commonwealth’s preferred narrative of white European discovery of previously uninhabited lands – under the doctrine of “terra nullius”– as a crime against humanity. For us, such revelations as Banks being rather an opportunistic creep – specifically in terms of his sexual predation on numerous Indigenous women unfortunate enough to come into contact with his spirited exertions for scientific discovery – are not so unexpected.

Neill traces Cook’s journey himself, crossing the Pacific Ocean to the places Cook visited and to speak to people along the way. Photograph: Foxtel

In place of the routine colonial narrative,this series flips perspective, presenting viewers with little-known First Nations histories of the voyage, most notably in a scene that occurs on a K’gari headland as the Endeavour tacks just off the coastline. A song – passed down through generations of the Butchulla mob – records the encounter from on-country that day:

Strangers are travelling with a cloud

It has fire inside, must be a bad spirit

It’s stupid, maybe, it’s going directly to the serpent place

This is the truth I bring

It is breathing smoke rhythmically from its rear

Must be songmen and sorcerers

Coming up and going back like a sand crab

The sea carried this ship here, why?

Further up the coast, Cook’s journals record the local mob calling out loudly and frantically waving as the Endeavour tacks close to the shoreline. It never occurs to him that the natives were attempting to warn him about something ahead. But by this time, Cook isn’t even listening to Tupaea anymore. He and Banks know all. Commendations from the Admiralty and Royal Society await them upon their arrival back in Blighty. The Endeavour is chocka with stolen artefacts and specimens. New lands and resources are about to be claimed “under the [Union] Jack” in the name of their king. They are the potent embodiment of Britannia – and proceeding full sail into the reefs ahead.

• The Pacific: In the Wake of Captain Cook with Sam Neill screens on Foxtel’s History Channel, Mondays at 7.30pm