The United States is rarely bashful about its showpieces. After all, this is the land that gave us the skyscraper, supersizing and Donald Trump’s toupee (allegedly).

However, one superlative is almost bound to stump people: the country’s largest national park. Try asking a friend to name it. The Grand Canyon, they may say. Yellowstone, perhaps. Throw in a few clues. Mention it is so large it would swallow Switzerland whole and have room for a sizeable principality for dessert. Even drop in the fact it is in Alaska. The overwhelming chances are you will still see a blank face before you.

Perhaps it is not such a surprise. Wrangell-St Elias National Park had roughly one annual visitor for every 200 acres at the last count. Stretching from the coast to the mountainous interior of the “Last Frontier” state, it is remote and hard to access.

Intrigued by this vast unknown, I set off with three fellow adventure-seeking spirits to explore. After a few hours’ drive from Anchorage, we reached a dusty airstrip alongside the state’s mighty Copper River, where the season’s first salmon were surging upstream.

We encountered our first superlative before we even arrived in the park: Kelly, our weather-beaten bush pilot, was also the world’s most laconic man. As we took off and the sandbanks fell below, he gestured towards an ominous cluster of grey on the southern horizon. “There’s something of a typhoon coming in,” he told us, leaving the intercom to crackle for a moment. The plane wobbled. “I don’t think it’s going to hit us, but that explains all the wind.”

Then Kelly fixed the Cessna 206 on its course east, threading through a mountain range that seemed never to end. His commentary turned to the park’s extraordinary alpine beauty, comprising nine of the 16 highest peaks in the US. Over there was the highest point of the Wrangell ranges, Mount Blackburn, and the active volcano Mount Wrangell. “We sometimes see steam coming out – glad we don’t see it too often, we live a bit too close,” said Kelly.

This was truly wild country, ripe for adventurers, where you are far more likely to meet a bear than another human. Kelly pointed at a river that only one intrepid soul had navigated; an intimidating peak that only one climber had summited. We could just about make out a gravel track weaving through the bush below, too roughly hewn for most car rental companies – hence our use of the services of Wrangell Mountain Air.

Soon a wide valley spread out before us and we looped over a glacier – the park is home to the highest concentration of these mighty ice rivers in North America – before approaching another long, dry airstrip. “I usually come in the other end, but the windsock is blowing some,” Kelly explained.

This was the tiny hamlet of McCarthy, our base and a compelling place in its own right. As improbable as it seemed in the wilderness, it was once a boom town, where money flowed easily, even in the depths of the Depression, as nearby copper mines thrived.

It was set up as fast-living and freer alternative to the rigidly regulated company town , and a cast of big characters passed through in its heyday: labourers, chancers, alpinists and bootleggers – although few larger than a 25-stone prostitute named Beef Trust who once, reputedly, plied her trade here. When the mines collapsed in 1938, it withered to a ghost town. Decades on, a few hardy souls ventured back to the area: outdoorsmen, homesteaders, then tourist workers and, yes, a quota of oddballs.

We checked into Ma Johnson’s Hotel, a wonderfully authentic Wild West-style lodge on the main street, then strode, ruggedly we hoped, for our first taste of the great outdoors.

Two hours later, slightly less manfully, I was paddling vigorously and not altogether coherently on an inflatable two-man “duckie” kayak on a glacial lake. Once my co-paddler and I had established our craft was practically unsinkable, we moored with the rest of the group on an “island” – in fact an iceberg – in the middle of the lake. We toasted several capsize-free minutes in what is likely to be my only ever coffee break on a large chunk of ice, listening to cracks and splashes as the glacier thinned.

Back in McCarthy, we explored some more, sharpening our impression of an abandoned outpost. Many old wooden shacks were derelict; chassis of old pickup trucks lay rusting by the wide, dusty streets.

Today its residents are frequently outnumbered by moose, with just a few dozen hardy souls living here year-round – although the population swells to several hundred in the summer. One of the full-timers was our host, Neil Darish, and nobody could accuse him of being bashful about Wrangell-St Elias. “More superlatives than any other national park,” he told us.

An East Coast sophisticate – a slightly incongruous find in Alaskan backcountry – Darish already seemed to own half the going concerns in town, many aimed at tourists. The fine-dining bistro, the bar where we drank, and the hotel we stayed in, all belonged to him.

He had another more controversial way of shining a spotlight on his home: a pivotal role in Edge of Alaska, a reality television show that had just finished filming series two (“Hidden deep in the wilderness of Alaska is the toughest town in America: McCarthy”). Some locals welcomed the attention; others derided the tabloid approach. “It’s pretty ridiculous,” one told us.

That said, the human history of the national park can be far-fetched. A man with a suitably low-key nickname, “Tarantula” Jack Smith, bears much of the responsibility. A prospector in the early 20th century, he discovered huge copper deposits, news of which landed on the radar of the Guggenheims and JP Morgan. They ploughed in vast sums, funding one of the world’s most unlikely railways, a 196-mile track traversing raging rivers, glaciers and canyons.

A view over Kennecott in the Alaskan wilderness

We saw the legacy of the remarkable Copper-River Northwestern Railway, as the project was known, on a guided tour of Kennecott, the abandoned mining town the railroad was built to serve. It is an extraordinary, evocative place, strewn with buildings in disrepair: an old company store, school, bunkhouses, a power plant, administration buildings and one of the most advanced hospitals of its time, including the first X-ray machine in Alaska.

All sprang from copper wealth, and all were deserted when the mines shut, their decay arrested only by the extreme cold and dry of the climate. The centrepiece is the copper mill, one of the largest free-standing wooden buildings in the world. We followed our guide, Bryan, up to its summit, where workers would make a hair-raising commute on a “tram”, a rudimentary cable-car bringing ore down from the hills. They would cling on for the numbing return journey to the mines. Thoughtfully, the company issued a disclaimer saying it was all at their own risk.

But they got the results. Ore passing through the mill’s 14 storeys of gravity-defying timber, and the tanks of the leaching plant opposite, made the Guggenheims’ and Morgans’ “Alaska Syndicate” a fortune: $100 million in profit in little more than three decades. For context, Russia sold the whole of Alaska for $7.2 million in 1867.

Walking beyond Kennecott, we left these giant totems of the previous century behind and rejoined the wild. Spruce and cottonwood lined a path, lupins on the fringe, with the Kennicott Glacier below (a careless clerk caused the variant spellings of the mine and the glacier). We passed a dilapidated wooden outhouse, its door pinned with a handwritten warning, “Beware: the porcupine may actually be in the hole”, then descended to yet another ice river, the Root Glacier.

Root Glacier

Here we donned crampons and stepped on to the ice. We crunched over the ripples, eddies and hypnotic frozen swirls, a close encounter with the fascinating geology of a glacier: its peaks, lakes, moraines and rivers partly shaped by its age-old collision course with the Kennicott. In this dramatic setting, Bryan had more tales of derring-do. He picked out Mount Blackburn from the summits beyond and told us how it was first climbed by a female alpinist named Dora Keen in 1912. She had roped in local prospectors on her mission to the top, and only one had made it to the top with her. She married him later in McCarthy. “She was a badass,” said Bryan approvingly. “A real cool chick.”

Like the landscapes, tales from these parts tend towards the epic, we had realised. When time came for a return to more mundane realities, such as paved roads and Wi-Fi, we went back to our aircraft at McCarthy airstrip. It was a still day as we took off, soaring above glacier and spruce, and leaving the mighty old copper mill on its unlikely perch in the wild.

Getting there

Icelandair (Icelandair.co.uk; 020 7874 1000) offers the fastest route to Anchorage, Alaska (via Reykjavik) from Gatwick, Heathrow, Manchester and Glasgow. Return flights from £653.

Discover the World (01737 214291; discover-the-world.co.uk) has a 14-night “Alaska’s Natural Wonders” tour that includes Alaska, Seward, Denali, McCarthy and the Knick River. Prices from £2,430 per person based on two people sharing, excluding international flights.

Bridge & Wickers, part of the Ultimate Travel Company (020 3553 0379; theultimatetravelcompany.co.uk), has a 15-day “Alaska’s Mountain Peaks and Glaciers Itinerary” that includes Anchorage, Seward and Denali National Park. Prices from £3,600 per person, based on two sharing, including flights.

More information

See travelalaska.com.

For Telegraph Travel’s guide see telegraph.co.uk/alaska.

Download the free Telegraph Travel app for an overview of America’s 57 national parks provided by our experts. See telegraph.co.uk/travelapp.

Alaska's other national parks

Despite having almost two-thirds of national park land in the United States, Alaska only accounts for a fraction of the visitors. Here’s an outline of the seven other national parks in the state (leaving aside the confusing array of historical parks and monuments that also come under the National Park Service remit).

Obama in Kenai Fjords National Park

Kenai Fjords

One of the more accessible of Alaska’s parks, right, this features as a stop in cruise itineraries, docking in the tiny port town of Seward. It is known for its dramatic fjords and multiple glaciers. This was the national park that President Obama visited last spring. Paddle-boarding off Bear Glacier with Liquid Adventures (001 907 224 9225; liquid-adventures.com) is an extraordinary experience (beginners welcome).

Gates of the Arctic

One of the least visited parks in the entire National Park system, entirely north of the Arctic Circle. You are more likely to encounter caribou or grizzly bears on the fragile tundra than other tourists.

Katmai

Known for its fantastic opportunities to see brown bears, mostly from the comfort of a lodge, as they scoop up salmon. Katmai is mostly accessed by plane or boat and lies about 290 miles south-west of Anchorage.

Denali

The highway north from Anchorage makes this the most visited national park in Alaska as well as the draw of its eponymous peak – previously known as Mount McKinley, left – which at 6,194m, is the highest in North America. Take a flight-seeing tour with Rust’s Flying Service (flyrusts.com).

Glacier Bay

The most southerly of Alaska’s national parks – regularly visited by cruise ships – this has millions of acres of rugged mountains, dynamic glaciers, temperate rainforest, coastlines and sheltered fjords.

Kobuk Valley

Such is the remoteness of this park in north-western Alaska that, remarkably, absolutely no visitors were recorded here for the past two years. There probably were tourists to see the sand dunes and caribou migration route the park is known for – just no one there to note them down.

Lake Clark

Just 100 miles from Anchorage, no roads lead to this park, above, which includes the junction of three mountain ranges, a coastline with rainforests, alpine tundra, and its fair share of glaciers and salmon-filled rivers.