It is easy to detect other reasons why Cook's prestige has been challenged. For generations Australian history was viewed, mistakenly, as starting with the procession of European sea explorers, with Cook himself so prominent in that procession. But once the long Aboriginal history of this continent was taken seriously, and the fruits of new research poured in, the sea explorers justifiably had to move down a step or two. Moreover, Cook is seen by many Aborigines as the symbol of the British invasion.

And then there is the startling Chinese challenge to Cook's place. The recent book by Gavin Menzies, a Briton, is highly readable and widely read here. In 1421 he claimed that, long before the first Dutch sailed by, a Chinese fleet discovered Australia and New Zealand. It is now realised that his evidence and his chronology do not stand up to inspection. Thus the first Chinese at the Queensland town of Gympie did not appear there as voyagers in the Chinese admiral's great fleet in 1421, but arrived four centuries later as gold seekers and latecomers. The theory of a Portuguese discovery of Australia has more promise, but lacks supporting evidence.

In recent years my curiosity about Cook was reawakened by a visit to the tropical riverbank at Cooktown, where his leaky ship was repaired, and by voyages to remote places he had found. And then in March 2006, at the new docklands in Melbourne, I went aboard the life-size replica of his ship and, like so many other visitors, marvelled at the cramped spaces. You have to crouch in order to walk. A quick calculation - I hope it is accurate - concluded that more than 20 Endeavours could be crammed side by side into one soccer pitch.

Brilliant as he was in his explorations of what he called a sea of dangers, he almost wrecked his ship on a coral reef in north Queensland. For this near-disaster his great biographer, the late J. C. Beaglehole of New Zealand, virtually absolved him from blame. But he was sailing in the deceptive light of the moon. After perusing closely the sea journals kept by Cook, I found out that in the south-west Pacific this was the third night on which he courted and found grave dangers while sailing in moonlight. Almost certainly he would not have hit the reef if he had been sailing in daylight.

His crew ultimately paid a high penalty for this mishap. Their ship, roughly repaired, limped through Torres Strait, one of Cook's many remarkable feats of navigation, and finally reached the Dutch colonial port of Batavia, now called Jakarta, where the Endeavour spent weeks undergoing repairs. There malaria and dysentery did their damage, and in the following months almost a third of Cook's crew died. Cook was more conscious than his latter-day admirers of the devastating effects stemming from the damage to his ship at the Great Barrier Reef.

And yet, when you compare Cook with his main French rival, you realise his astonishing talents. Captain Jean de Surville is virtually unknown in Australia but he too was searching, at the same time as Cook, for the missing lands that were believed to lie somewhere in the vast unexplored ocean between Australia and South America. De Surville believed that a Jewish settlement lay in or near that missing continent; and he sailed from India to find it. His ship, St Jean Baptiste, twice the size of Cook's, was loaded with trading goods.

De Surville reached the vicinity of Sydney five months ahead of Cook, but he did not go ashore. He was a trader in a hurry. He sailed on to New Zealand, where he almost met Cook off the northern coast of North Island, and then sailed east in a fruitless search for the Jewish settlement. De Surville had his achievements.

Scurvy was one reason why the Frenchman failed and the Englishmen succeeded. The French ship lost scores of sailors from scurvy. Cook lost not one sailor to the terrible illness that arises largely from a deficiency of vitamin C. The weekly journals kept by the French officers reveal the growing shortage of able-bodied crew and expose the powerful truth: if Cook had not so effectively maintained his crew in sound health, he would have had to turn back long before he reached eastern Australia.

Then again Cook and several of his crew were usually - but not always - highly skilled in calculating longitude, or their exact position on an east-west line. By standards of the time, their maps and charts were wonderful, while de Surville sometimes was 200 sea-miles astray in his calculations. That explains how those who later read his journals did not realise how close his ship came to Sydney Harbour.

The young scientist Joseph Banks kept a fascinating journal, day after day. We used to wonder why he first thought rather poorly of NSW but praised it so highly when he resumed his life in England. I think I see why he changed his mind. Calling at Cape Town on the homeward voyage, he marvelled that under the labours of the Dutch and their coloured servants, a few tiny patches of good soil set amid a wasteland of inferior soil could be so productive.

Botany Bay became in his eyes another Cape Town. Banks used to be hailed as the father of NSW because it was on his recommendation that the British decided to send the first convicts to NSW, but he too has tumbled down the Australian ladder of popular fame in the past 40 years.

One fact is beyond dispute, however. In 1770, Cook and Banks used their eyes and experience more effectively than any previous visitors to Australia. Without their visit, and the knowledge gained, Arthur Phillip and his first fleet would not have landed marines and convicts in Sydney Cove 18 years later, and the history of Australia and New Zealand would have been very different.

Historian Geoffrey Blainey's latest book is Sea of Dangers: Captain Cook And His Rivals