The headless corpse is buried in gravel for up to 12 weeks while the poisons (trimethylamine oxide and uric acid) leak away. Then it is hung for several months until a brown crust forms. It is tantalising to imagine the trial and error, let alone the desperation, involved in perfecting the centuries-old process of making hákarl, an Icelandic dish of fermented shark.

Most non-Icelanders recoil in horror without even trying it. The stench from my slimy, chewy stash drifts into our kitchen, even when stored quadruple-wrapped in the freezer. The taste recalls the strongest cheese you have ever eaten, left on a rubbish dump for several days in hot sun and doused in sea-water. The neophyte’s tastebuds are begging for mercy even before the gag reflex kicks in.

Even Agnar Sverrisson, an inveterate promoter of his native Iceland’s trendy new Nordic cuisine, watched with some bemusement as I gobbled hákarl in the private dining room of his Texture restaurant in the heart of London’s West End. Eventually he asked if I would like to take it home with me.

Iceland’s traditional cuisine is born out of centuries of exigency. Poor soil and a harsh climate means sparse harvests, and preservation trumped taste. Modern times are easier. Sverrisson recalls being given hákarl as a childhood TV snack – the Icelandic equivalent of popcorn. Now even his daughter flinches at the smell.

But a trip to the fish market in central Rejkyavik still assaults the senses and stretches the imagination. Our short shopping list included ábrysti (cow’s colostrum, which looks like orange juice and is favoured by body-builders), hrutspungar (whey-pickled rams’ testicles), hvalspik (whale blubber) and seal flippers.

The best time to experience the widest range of Icelandic food is in the month of Þorri (mid-January to mid-February in the traditional calendar) when families convene for the Þorrablót feast (the Icelandic letter Þ is pronounced with a hard “th” as in “therefore”; the ð is a soft “th” as in “think”). Like most traditions, it is a modern invention, dating from the 1960s, when a Rejykavik restaurant started popularising previously despised peasant foods. Blood sausage (blóðmör) and liver sausage (lifrapylsa) feature strongly. So does the national version of haggis, called slátur (literally “slaughter”) which combines sheep intestines, blood and fat with oatmeal and rye flour. Svið (a halved sheep’s head, singed and boiled) is a particular delicacy: the eyes, tongue and ears are eaten, but, for hygiene reasons, not the brain. The same taste in a less daunting format comes from svíðasulta (brawn). Cured lamb hearts are nicer than they sound but most delicious of all is hangikjöt (lamb smoked over a sheep-dung fire), which is a kind of ovine prosciutto.

At this point, the visitor may start realising that whatever his eyes may be telling him, Icelandic food is mostly rather enjoyable. Sheep in particular are one of the highlights. Unlike the bland, mass-produced Antipodean lamb which most people in the industrialised world are used to, the meat is gamey with a faint taste of seawater and moorland. The animals eat wild herbs, berries, moss and seaweed, all of which feature in Icelandic cookbooks too. The local horsemeat has a similarly distinctive taste too.

One’s conscience may tingle there, or at other points. We ate whalemeat carpaccio, (texture like beef, taste like tuna). It comes from the minke whale, which is not endangered. Smoked puffin breast was good too (quail breast with a maritime note), but though the birds are plentiful for now, their numbers are dropping. The highlight was melt-in-the-mouth smoked shag (the local cormorant). Imagine the best-ever smoked salmon, but crossed with goose-breast carpaccio.

Desserts highlight the Nordic fondness for the cosy, healthy and natural. Rye bread ice-cream is good, especially with local rhubarb jam. Skyr is a national treasure: a low-fat soft cheese that tastes like a particularly creamy yoghurt. Try it with moss syrup.

Only alcoholic drinks are a bit of a disappointment. Alcohol was frowned on for years (the sale of beer was legalised only in 1987). Kvöldsól is a sweet wine made with crowberries, and a blueberry liqueur has attracted a small following. But the main national drink is Black Death, a fiery spirit made from fermented potato pulp and flavoured with caraway seeds. That it is usually taken to douse the aftertaste of hákarl tells you everything you need to know about both products.