At the age of eight, my daughter Nina does not have a strong sense of species differentiation.

On the sweaty drive to Oban, she spent most of the time on her toy mobile phone, texting friends, family and the Ood, who are, as Doctor Who fans will recall, creepy aliens with multitentacled heads and extensive supernatural powers. Strikingly like creatures of the deep, we could agree.

But, I reminded her, the point of our break in Mull was to see real, living whales, porpoises, seals and puffins. We were to learn about their feeding patterns, predators and breeding and to come back relaxed, revived and full of eco promises.

It was not to communicate with intergalactic life forms and then go in the huff.

We were to spend two days out with Sea Life Surveys, a family-run, Mull-based firm that combines tourist boat trips with research into the minke whales and other cetaceans who inhabit the waters around the Inner Hebrides.

Day one was an eight-hour whale-watching marathon on board the Alpha Beta with eight other binocular-toting, cagoule-wearing wildlife enthusiasts.

A joy for those with sturdy sea legs and 20-20 vision, but, in retrospect, overambitious for a pair of shortsighted landlubbers. Nina was too poorly to drink her hot chocolate, threw up her ginger biscuit and spent a good deal of the trip below deck, curled beneath a fleece.

I did not fare much better and had to retire to a quiet spot at the bow where I could doze queasily, sitting up only to peer at harbour porpoises playing with their calves, minkes feeding and an unfeasibly cute puffin swimming along in our wake with a bill full of sand eels. Such are the hazards of pursuing nature’s greatest creatures.

Lunch was sandwiches on Muck, a crumb on the map between the islands of Eigg and Rum. Here it’s all corrugated iron lean-tos and lethargic poultry, a scene that makes Mull look like Las Vegas. And although we tottered up the pier looking distinctly green, a stroll, a sit-down and a can of organic ginger beer from the extraordinarily well-appointed tea room soon had us feeling ready for the return journey.

The next day’s four-hour jaunt was much more obviously a commercial undertaking. The boat was bigger, the teenagers bored and the toddlers restless. This made no difference to the fantastic basking shark that popped up in the distance.

At the first sighting of the dorsal fin, Nina forgot her beloved Ood and rushed to the side of the boat for a better

view. I can’t have been the only adult playing the theme from Jaws in my head. In the still water, with enough cloud cover to cut the sun’s glare, we had a superb view. Once our eyes had grown accustomed to the light, we could see its tail fin and, as he opened his mouth to feed, his nose poking in and out of the water.

With the engine off, we drifted, and he disappeared only to reappear on the other side of the boat, close enough to touch. Not that anybody was volunteering.

The shark’s huge, rust-mottled, prehistoric grey body was clearly visible just below the water’s surface. Although they can grow to 12m, this one was not such a whopper. His mouth, however, was on a scale unlike anything I have ever seen.

He obligingly opened it very wide, giving us a good look at tiny vestigial teeth and the rib-like bones that arch along the roof of the mouth. A basking shark can, our guide assured us, filter the plankton from an Olympic-sized swimming pool every hour — if there were any plankton in the pool, and the attendant was foolish enough to sell the shark a ticket.

This one hung around for so long that we began to get blasé. The porpoises playing in the distance suddenly seemed more exciting. Eventually, he slunk off.

Word came through on the radio that there were minkes off Ardnamurchan Point, the spot where we had seen them yesterday.

It would be a bit of a run for no guaranteed whales, but did we want to give it a go? The democratic republic of Naturewatch decided that yes, we would.

Half an hour or so later, sure enough, the distinctive shape appeared in the distance. I could even identify the difference between the shallow dips it made to lunge feed — scoop whatever is edible from the surface of the water — and the sharper, elbow bend it made to do a deeper dive, when it can stay under the water for as long as 20 minutes.

My day of nausea had not been wasted after all. Had it been raining, I would have worn my anorak with pride.

Details: Sea Life Surveys runs various boat trips and packages (www.sealifesurveys.com). Accommodation is available at the Bellachroy inn, Dervaig (www.thebellachroyhotel.co.uk), with double rooms and breakfast from £37.50 per person per night.

Ferries leave Oban for Mull every two hours in the summer season (www.calmac.co.uk).

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