But this fails to strike terror into the Delhi weekenders and Western tourists strolling down to the riverside to spot terrapins, kingfishers and wading birds. They are smug in the knowledge that the most fearsome local reptile is the gharial - otherwise known as the fish-eating crocodile.
They have another, more urgent reason for caution. Nearly 100 tigers still roam wild amongst the plains and temperate jungle of the park. The days of the notorious man-eating big cats are now history, but to the people of northern Uttar Pradesh the memories are still fresh.
Kamal, the driver of my jeep for the afternoon, has made over 140 tiger- sightings during his 18 years at the park. Maybe he'll bring us luck. We have left our vehicle to go crocodile-watching. From a cliff-edge overhanging the river you look down onto a deep pool, carved out of silvery stone by the ice-cold meltwater from the hills. The crocodiles are out of sight, hiding from the cloudy weather. Deer grazing by the river bank look up, making alarm calls. Kamal puts a finger to his lips. "Tiger," he whispers. No further encouragement is needed for a rapid return to the jeep.
Kamal tells the legend of the Rudraprayag leopard, which killed 100 men and women - "before Jim Corbett shot him dead".
Which introduces the major paradox of Corbett National Park. This huge expanse of protected habitat was established in 1936 by English military man Jim Corbett, whose previous claim to fame had been his remarkable aptitude for slaying the local fauna. He nearly wiped out all the tigers in the region before he developed a subsequent interest in conservation.
Now Corbett is only one of nine national parks in India where tigers still live freely - thanks to the 1970s Project Tiger, when Indira Gandhi's government made a concerted attempt to save the species from extinction. For this purpose, the local inhabitants were evicted and their villages destroyed. Now human visitors are kept to a minimum in two ways. Firstly, the entry prices are high by Indian standards. For travellers accustomed to spending around pounds 1 per night at comfortable backpacking accommodation elsewhere, it seems steep to fork out pounds 6 entry and pounds 2 per night for military- style bunk lodges. Secondly, visitor quotas are strictly enforced - we were very lucky to get in without any advance booking.
So we spotted few humans at Corbett. If you want to see the usual tourist's India, don't go. The park is tranquil. There are no bazaars, slums, temples, traffic jams or roast-peanut vendors. The hills have not been sliced into the terraced fields which cover the Himalayan foothills. Instead, the park is a reminder of another age, before the countryside of India was tamed by farmers. We took an elephant ride through the forest - two hours for pounds 2 - listening for bird calls as our steed lurched through shoulder- height undergrowth. The towering white trunks of the ubiquitous sal tree were shaded by the green canopy, but as morning broke the light seeped between the pale pillars to startling effect. The twentieth century seemed distant. Our guide took us to tiger footprints and fresh kills. We even heard a strangely high-pitched tiger call, which caused some excitement.
Dhikala, with the most accommodation in the park, boasts the best panorama. From the reasonably priced restaurant you have a view which sweeps past the river across a golden plain reminiscent of East Africa. There are several birdwatching towers a short walk from the camp. You're certain to see wild boar, parrots, birds of prey and countless deer. But don't presume that you will see a tiger.
One tourist I spoke to complained about her fruitless tiger searches. "I don't know why they call it a tiger park," she moaned. "Maybe there aren't any and it's all a big con." But I felt reassured by the invisibility of the cats - it suggested this wasn't merely a giant zoo.
Corbett National Park is not an obvious destination for European travellers to India - I only met three other westerners. But Ramnagar, where you must book your stay, is only eight hours by train from Delhi (under pounds 2), so it is easily accessible. Buses leave Ramnagar every afternoon and return each morning, or you could hire a jeep for the day (pounds 12 plus).