Matthew Dennison is fascinated to see how western artists fantasised the flora and fauna encountered on three British voyages of exploration to the Pacific.

The son of a Liverpool leather-worker, George Stubbs had neither visited Australia nor seen at first hand marsupial life when Joseph Banks presented him with the pelt of a small female kangaroo late in 1771. Banks’s commission to Stubbs resulted in the first depiction of a kangaroo in western art.

The Kongouro from New Holland wasn’t painted according to Stubbs’s usual working practice. He never saw a kangaroo in the flesh. Instead, Banks arranged that the pelt he had acquired the previous year either be stuffed or inflated. Beyond that, Stubbs was forced to rely on hearsay and some roughish-sounding travellers’ sketches.

The image he created has a plump monumentality that suggests a degree of over-inflation or over-zealous taxidermy. Glimpsed against a theatrical backdrop of hazy mountains and pink-flushed clouds, Stubbs’s kangaroo makes up for in charm what it lacks in athleticism. Its novel exoticism is balanced by a passing resemblance to a hare.

Wholly unintentionally, the artist created an icon of Australian identity at the dawn of that country’s emergence into the European consciousness. At the same time, in a single memorable image, England’s leading animal painter effectively neutered that barbarous, unchartered landmass.

Stubbs’s painting is one of two acquired late in 2013 by the National Maritime Museum (the other is of a dingo: in this case, there was no pelt, inflated or otherwise, and Stubbs’s painting depicts in profile an animal akin to a dark-coated fox, a misleading glimmer of vague benignity in its single green eye). The museum has acted quickly to showcase its new treasures. Its chosen vehicle is the present small-scale exhibition, an examination through 36 images of the part played by artists in the three voyages of discovery undertaken by Capt James Cook.

Cook travelled to observe the transit of Venus from Tahiti in 1769; more significantly, he took the opportunity of claiming Australia for George III. From 1772 to 1775, he attempted a circumnavigation of the globe from west to east and, in the process, discovered New Caledonia and the South Sandwich Islands. In 1776, he was tasked with finding a north-west passage through the American continent from the Pacific to the Atlantic. That journey cost him his life, albeit not until he had reached the furthest northern point yet attained by a European explorer.

Cook’s voyages were concerned with exploration on more than one level. Banks, a botanist, accompanied the first, with the result that some 30,000 dried plant specimens were sent home and almost 1,000 botanical drawings undertaken by Sydney Parkinson (two are included here). Subsequent voyages were recorded by artists William Hodges and John Webber. The present exhibition features work by both men, particularly the former.

Hodges’s output included on-the-spot views as well as grander, more finished paintings. Among his subjects are eloquent images of Tahiti, Easter Island, New Zealand and the Cape. All conjure up for western eyes a paradisiacal dream world shaped by the Classical landscape painting of Richard Wilson and ultimately Claude Lorrain. In a characteristically 18th-century muddle, Hodges’ vision combined topographical exactitude and the Enlighten-ment spirit of rational enquiry with a romanticising impulse that recalls the fantasy party islands of Watteau’s paintings.

A Waterfall in Tahiti of 1775 apparently transplants European tree life into an idyllic faraway glen flooded with sunlight and lightly tufted with palm trees. Tahiti Revisited, painted one year later, is assertively exotic as strikingly alien to English eyes as the New Zealand landscapes of the ‘Hobbit’ films to our own generation. This is an exhibition of col-lisions, encounters not only of cultures, but also of  ways of seeing.

Webber’s portrait of Poedua, daughter of an Ulietean chief, may be the first European image of a Polynesian woman, but the artist chose to pose her as a dusky-skinned Venus, her classically derived stance a conceit borrowed from contemporary portraiture.

So heavily indebted to Classical reliefs is Johann Zoffany’s The Death of Captain James Cook, 14 February 1779, of 1798, that it’s easy to overlook the fear on Cook’s face. In Webber’s A Party from His Majesty’s ships Resolution and Discovery shooting sea-horses, latitude 71 North, 1778, even the fury disappears in the artist’s urgency to convey in comprehensible visual form an encounter between boatloads of sailors attempting to shoot walruses to eat and the animals themselves, bovine in their unconcern.

The crew were at odds over the attractions of walrus meat as a food-stuff. Their lack of conviction adds a theatrical quality to this delightfully odd painting and possibly serves as a metaphor for early Anglo-Pacific relations in an exhibition that reveals both colonial acquisitiveness and disquiet in the face of the unknown.

‘The Art & Science of Explor-ation, 1768–80’ is at The National Maritime Museum, The Queen’s House, Greenwich, until July 2015 (the Stubbs paintings on show until March 2015) (020–8312 6565; www.rmg.co.uk)