The grizzly bears appeared when we were least expecting them. One moment we were drifting down a blue-green river of glacier meltwater and enjoying the sunshine, the next, one of our companions shouted: “Bears!” And there they were: a mother grizzly and her two cubs bustling along the riverbank, writes Joanthan Grun.

Grizzlies are killing machines – they can rip you to pieces, they can run faster than a man, and they can climb trees. There is no hiding place. But we were separated by a stretch of water – although they can also swim – and this beautiful but deadly animal was not interested in us. Casting maternal glances over her shoulder, she led her adorably cuddly offspring in search of a meal of salmon. It was a magical moment on a holiday that was like stepping into a David Attenborough wildlife documentary.

As we drifted down the Kenai river, bald eagles kept their beady eyes on us and thousands of spawning salmon swam beneath us in the chilly, translucent waters.

A holiday to Alaska really is the journey of a lifetime, especially if you combine a land tour with a cruise. We spent the first week of our Princess tour travelling through the vastness of Alaska’s interior, with every day bringing a new memory to last a lifetime.

Then we spent another week on board the Coral Princess cruise liner, exploring the stunning coast with its teeming wildlife, and watching the glaciers tumble into the sea.

We flew to Anchorage to join our tour party on a crystal clear day. Our guide pointed out Mount McKinley, at 20,000ft the tallest peak in north America – it was a staggering 280 miles away.

You learn to treasure such days in Alaska – in the short summers the weather can sometimes be warm and welcoming but then the next day the rain may lash down.

In some places it rains almost all the time but that adds to the wild, unspoilt beauty of the state. Having said that, this is one summer holiday that needs a full range of clothes.

Princess operate a number of lodges in Alaska and we spent our first few days at the smallest property, on the Kenai peninsular. You stay in delightful wooden cabins – each with a wood-burning stove.

The lodge comes to life for the Alaskan summer and is then mothballed for the long, dark winter, leaving the countryside to the tough, independent-minded local residents who make do in harsh conditions that British people can only wonder about.

The sun had given way to grey skies and mist when we travelled from Kenai to the port of Seward for a day-long cruise around the Kenai Fjords National Park.

In a few short hours our breath was taken away by the wildlife: humpback whales emerging out of the mist to dive in front of our boat, their fishy breath hanging in the air; lolling seals; angry sealions arguing with each other, even mating sea otters. And puffins so full of fish that they could not get airborne.

And then the air temperature plunged and out of the mist loomed the Aialik Glacier. No photograph or high-definition television picture can truly represent the majestic beauty of a tidewater glacier as it flows into the sea. The Aialik Glacier towers higher than St Paul’s Cathedral and on days when the weather is overcast, a trick of the light turns it blue. Really blue – breathtakingly blue.

Our ship was expertly piloted to the very edge of the floating ice at the foot of the glacier, so that that towering wall was about a quarter of a mile away.

The captain cut the engine, and for some minutes we watched and listened to the cracks and booms as pieces of ice the size of a house broke away and tumbled into the sea.

Next stop on the tour was the Mt McKinley Princess Wilderness Lodge, named after the towering mountain. It can be an elusive peak – often shrouded in cloud and some travellers may never see it.

Princess provides an interesting selection of excursions on its land tour and we set off in search of gold with local hunter and gold panner Nick Smoljan.

He regaled us with tales of shooting moose and delivering babies – he is also the local paramedic – as our van bumped along an unmade road and through a river before finally arriving at a beach where he reckoned we would find gold.

He was right – sifting buckets of mud and grit and then panning the residue revealed tiny flakes of gold. To whoops of child-like glee they were picked up with tweezers and delicately placed in little bottles to take home – souvenirs with a difference.

Then came the real wonder – as we drove back through the tundra, the sun burned off the clouds and there was Mt McKinley in all its glory, reflected in a lake in the wilderness.

Next stop was the Denali Princess Wilderness Lodge, which is right on the boundary of the national park that is home to Mt McKinley. We had travelled north, and the summer was rapidly ebbing away to be replaced by a stunning display of autumn colours.

It was here that we flew in a helicopter over the glowing autumn landscape to land on a glacier. The flight was thrilling and all the things you learned in school geography lessons about mountains and glaciers suddenly made sense.

Another day we clambered onto a school bus and a National Park guide drove us through the park on the lookout for wildlife. Suddenly, there was a a huge moose – in the mating season they are as dangerous as bears, so we watched from a distance.

Then it was time to head for our ship and we boarded a special train which trundled all day through beautiful countryside to the port of Whittier where the Coral Princess was waiting.

It carries just over 2,000 passengers in some style and has the sort of jump-to-it service that Americans demand, and there’s plenty to keep you amused.

The main restaurant offers quite exceptional service and for a supplement you can also treat yourself to the on-board Italian restaurant and the steakhouse.

And if you really feel like pushing the boat out you can eat at the chef’s table – a fantastic gastronomic dining experience that proves that cuisine on cruise liners is about quality rather than just quantity.

The Coral Princess made its way down the coast of Alaska towards its final stop at Vancouver.

For many people, the highlight of the voyage will be the visit to the Glacier Bay National Park, where glaciers crash into the sea, waterfalls cascade down rugged mountains and bears roam the deserted shores.

But then there were the whales. One of our ports of call was Juneau, Alaska’s capital. Our little tour boat headed past several humpbacks spouting in the autumn sunshine but didn't stop because one of nature’s most amazing spectacles was taking place a little further on.

There were 10 humpback whales hunting together using bubble net fishing – circling a shoal of fish and creating a net of bubbles to trap them. When the moment is right the whales rush to the surface, scooping thousands of fish into their jaws. Even the crew just stood and watched in silence.

Yes, Alaska is an amazing place and it is little wonder so many people dream of paying it at least one visit.

Alaska cruising Best for: watching whales, wildlife and wilderness.

Time to go: The all-too-short Alaskan summer.

Don't miss: barbecued fresh salmon.

Don't forget: binoculars for watching those whales.

Jonathan Grun was a guest of Princess Cruises which offers 13-night packages from August 21, 2012 from £1,947.

The trip includes a six-day land tour (Anchorage, Mount McKinley Princess Wilderness Lodge, Denali Princess Wilderness Lodge, Copper River Princess Wilderness Lodge) followed by seven nights on board Coral Princess via Anchorage, Hubbard Glacier and Glacier Bay, Skagway, Juneau, Ketchikan and Vancouver.

Fare per person based on two adults sharing inside stateroom, and includes flights ex-London (ex-Manchester also available), accommodation, all main on-board meals and entertainment.

Call 0843 373 0333 or visit www.princess.com