Swimming with dolphins. Everyone yaps on about wanting to do that before they die. But swimming with tuna? For some reason, when you tell people you're going swimming with tuna, they laugh in your face. It sounds inherently absurd, and I'm not entirely sure why. I think it's because we often encounter tuna in tins. Also – and I know this is a stupid thing to think, but it's hard not to think it – there's that smell. You expect tuna to smell like, well, to smell like tuna, even though they're still alive, still in one piece and, most importantly, they're underwater where you can't smell anything.

My lack of knowledge was, in retrospect, stunning. I figured the tuna was a fairly docile fish, probably about the size of a shoe. I was to be disabused of this and several other notions during my visit to Australia. But it wasn't "regular" Australia I was heading for. Most overseas tourists visit Sydney or the Gold Coast. I was bound for South Australia, an area that's often overlooked. Would this be the equivalent of visiting Britain and staying only in Croydon?

Adelaide quickly struck me as a superb place to live. It's clean, it's pretty and despite being the largest city in South Australia, it's easy to walk around. We stayed in a variety of eccentric and inviting heritage homes run by the equally eccentric and inviting Rodney and Regina Twiss. Staying in a house in a residential area would be frustrating in many cities; given the compact nature of the city, it's a great idea in Adelaide. After 24 hours, you feel like a local, even though you absolutely aren't.

Adelaide makes an ideal base for touring the region. For sun worshippers, there are beaches a short tram ride away; for alcoholics, the Barossa Valley lies just to the north-east; and for people who want to swim with tuna – or sharks – a short plane journey will take you to Port Lincoln. Australians seem to catch small planes like we catch buses. It takes less time to fly from Adelaide to Port Lincoln than to take the 159 bus from Streatham Hill to Oxford Circus. Unlike the 159, they serve snacks on the plane and nobody tries to stab you.

Charlie Brooker and his wife Konnie Huq relax on the beach after another day's hard work at sea: 'There may be photographs of me in a wetsuit accompanying this article. I urge you not to look at them. They will be images of overpowering sexuality.' Photograph: Kingsley Griffin for the Guardian

There's not much to see in Port Lincoln itself: its appeal lies in the water, in the scenery of Boston Bay and the fishing and diving opportunities there. Our tuna-swimming expedition was going to be part of a two-day "ocean safari" with Adventure Bay Charters, run by the affable Matt Waller. Once on board, we sailed to Matt's tuna farm (he's a fisherman, see) which essentially consists of a huge floating bowl made of netting – picture a giant sieve wafting in the ocean and you're not far off. At this point we had to don wetsuits. There may be photographs of me in a wetsuit accompanying this article. I urge you not to look at them. They will be images of overpowering sexuality.

Anyway, fact file: contrary to earlier statements, a tuna is not about the size of a shoe. It's massive. Bloody massive. It has cold, unknowable eyes and is covered in sharp scales. And it swims very quickly indeed, especially when you hold out a smaller, dead fish for it to eat. It leaps and snatches the damned thing out of your hand so fast, you can't even see it: it's like being mugged. Mugged by a fish. And the giant underwater tuna bowl teems with them. In summary: although "swimming with tuna" sounds inherently comic in theory, in practice it's bizarre, exhilarating and faintly scary.

From the tuna farm, we made our way to a nearby island, where we jumped off the boat to swim with sea lions. Sea lions are so outrageously cute, even I had to concede they were charming, and I usually vomit at the sight of rainbows. They were friendly, too, and swam alongside us, diving, rolling and generally behaving like something from a Disney film: almost like Care Bears of the sea, except, unlike Care Bears, you don't want to kill them with hammers.

Then it was on to a prime spot for great white sharks. The viewing cage went in the water, and I went in after it. I'll admit to being nervous at this point: having been shocked by the size of tuna, I was trying mentally to prepare myself for a moment of life-altering terror. Most tours toss buckets of bait into the water, whereas Matt has a more eco-friendly method of attracting sharks. He lowers speakers into the water and pumps out rock music. He claims great whites are particularly attracted to AC/DC.

Floating in a cage underwater, keeping watch for sharks like Richard Dreyfuss in Jaws, while simultaneously listening to loud, driving rock, is a uniquely surreal experience. It could have been bettered only by the appearance of an actual shark. Sadly, on the day, none was forthcoming. This didn't seem to be down to the music, incidentally: neighbouring boats, hurling berley into the water by the bucketload, were having no luck either. Sharks aren't predictable. If they were, no one would ever get eaten by them.

It's a measure of how much fun the rest of the ocean safari was that the nonappearance of the most fearsome creature on the planet wasn't much of a downer. The following day we visited another island to peer at a larger sea lion colony, caught fish, stuffed our faces and ate fresh oysters (once I managed to overcome my inherent fear of eating anything with a 1% chance of making me puke). Then it was back to Port Lincoln, the airport and Adelaide.

The next day, we caught another shuttle flight, this time to Kangaroo Island. Kangaroo Island sounds like a sarcastic nickname for Australia itself: fitting, in a sense, because it's almost like a compressed version of how Australia looks in your head as a child. It's known as Australia's Galapagos because of its abundance of wildlife. There are creatures everywhere. Kangaroos hop along the roadside, koalas laze in trees, echidnas shuffle through the undergrowth: it's like a huge safari park with no fencing.

We stayed at the Southern Ocean Lodge, a place so confidently swish and friendly, I instantly felt like a burglar. It's easily the most upmarket place I've ever stayed: I was almost ashamed to go to the toilet. The architecture is straight out of Grand Designs: all floor-to-ceiling windows and understated modernity, not to mention stunning views across the ocean – the lodge is perched atop a cliff, overlooking a beach, situated in between two national parks. If it housed a death ray (which I'm fairly sure it doesn't), this would be precisely the sort of place a taste-conscious Bond villain might construct.

Not that you're there to laze around indoors. A tour of Kangaroo Island is essential, particularly if your time is tight, as ours was. We were shown round the island by Rob Ellson, a former local newspaper editor turned tour guide. The nature here truly is bizarre and fascinating: not only the kangaroos, which, if you're quiet, you can sneak hilariously close to, but the plant life, and I say that as someone who yawns himself half to death at the mere mention of a stamen. Kangaroo Island has a species of tree that thrives following a fire: the Xanthorrhoea (or "Grass Tree", for those who prefer words you can actually pronounce) flowers and sheds seeds when burnt. It even flowers when exposed to smoke. Just as well: in 2007, a series of bushfires destroyed 95,000 hectares of woodland. Today, the casual visitor would be hard-pressed to tell where the flames had been.

It's hard to describe how relaxing a place Kangaroo Island is. There are so few people, so few cables and billboards and cars and buildings and things, that your mind soon starts to stretch out and lie down. It was almost like being deprogrammed. Accommodation isn't cheap, and it's easy to see why. Leaving the place was a wrench, like knowing you have to get out of bed on a cold morning and turning back beneath the duvet in a bid to get a few more moments of comfort.

Having never visited the other bits of Australia, I had nothing to directly compare South Australia with, but if the rest of the country gets any better than this, it's quite frankly taking the piss as a nation.

• Black Tomato can arrange an exclusive 12-night, three-centre trip to South Australia, taking in Port Lincoln, Kangaroo Island and Adelaide, from £4,199pp (based on two sharing). For more information on South Australia, go to southaustralia.com. For more information on Adventure Bay Charters, go to adventurebaycharters.com.au. For more information on Southern Ocean Lodge, go to southernoceanlodge.com.au. For more information on the North Adelaide Heritage Group, go to adelaideheritage.com.

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