I was delighted to see giant basking sharks on a recent trip to Scotland, but such moments of wonder are rare. Creating fishing reserves would allow our oceans to recover – and preserve this incredible feeling

I believe we possess a ghost psyche: a set of capacities that helped secure our survival in more dangerous times, but that now are vestigial. I picture this as a seam of intense emotion, buried so deeply in our minds that we can seldom find it.

I believe this because, on rare occasions – in all cases when immersed in the living world – I have been confronted with a set of feelings that are so rich, raw and thrilling, so different from anything else I know, but at the same time so strangely familiar, that I have had no way of reconciling them with the rest of my emotional life. I believe that on these occasions I have inadvertently triggered a kind of genetic memory, an ancient adaptation to the circumstances that once shaped our lives.

I encountered it one day when, roaming through a wood, I came across a deer that had just died and – foolishly, deciding to take it home – hauled it on to my shoulders. I felt it when stalking up a tidal channel with a spear, looking for flounders, and when I came face to face with a bison on a forest path in Poland. I experienced it when I first saw a minke whale in Scotland, and when a dolphin leapt over my boat in Cardigan Bay. And I felt it last summer in the Hebrides, kayaking with basking sharks.

The same feral ecstasy – a primal thrill mingled with ancient recognition – returned every time we saw them

The sharks were what drew me, my family and some friends to a small island in the Inner Hebrides. (I have chosen not to name it, since it is small enough to be overwhelmed easily and the ecology is sensitive. In any case, there are places throughout the islands where you can enjoy similar experiences.) Every year, sharks come to the islands, sometimes in ones and twos, occasionally in vast packs. A friend lent us his kayaks and advised us to hunt for them in the sound between the island and its eastern neighbour. As the tide rips through the strait, it funnels the plankton on which the sharks feed into dense swarms.

You can see that there is something special about the sound even before you take to the water. From the beach, I watched gannets pluming into the sea and long lines of cormorants paddling down the tide. Seals swam around the rocky islands close to the shore. Exploring the sound with a fishing rod, I found shoals of saithe (sometimes called coley or coalfish) 300 metres long. Though handliners and lobster potters work here, trawling is banned, because a fibre-optic cable runs between the islands. There is a hint of what the seas around Britain – once among the richest in the world – used to be like, and could be like again.

I didn’t know what I was looking for until I saw it. A flash of light, bouncing across a mile of sea, cut through the sparkle of the waves like a Morse lamp. The sun was reflecting off something that stood perpendicular to the water, something that came and went. It could only have been a fin. I marked the spot in my mind and paddled across the sound at ramming speed.

Facebook Twitter Pinterest ‘The sharks were what drew me’ ... Monbiot on a kayaking expedition in Scotland with his daughter. Photograph: George Monbiot

When I reached the place I had marked, I thought at first that I had come too late. All I could see was the steady progression of the waves and an occasional herring gull, hunting for fry. Then I noticed a broad, smooth scar on the water, a sign of turbulence below. I moved towards it. As I did so, a great, ragged fin rose from the sea. Three metres behind it, a tail scythed across the waves. I realised that the shark was circling towards me.

I knew that basking sharks are harmless filter feeders, but seeing so vast an animal coming my way as I sat in a tiny plastic boat provoked a moment of panic. I thought it was going to hit me, but the tail swept around again and passed just in front of the prow. My terror vanished. I watched the great snout go by, followed by the flaring gills, then yard after yard of the grey barrel body, brindled by the light refracting through the waves, almost scraping the boat.

After the shark passed me, it dived. I turned the kayak, scanning the sea, then saw the flash again, 100 metres away. It was the same fish – I recognised the dorsal fin, damaged perhaps by a propeller. As it circled, I cut across the arc. Again, it approached head-on. This time it did not turn. I saw the cavernous white mouth, perhaps a metre and a half across, bearing down on the boat. It passed straight underneath me. I noticed the scars on the skin, and, close to the tail, a remora, a fish mostly confined to the tropics that attaches itself to large animals using a sucker on the top of its head. This one must have travelled thousands of miles with its host.

As I anticipated the shark’s movements, placing myself in front of it, it passed close to the boat again and again, once gently brushing against the hull. It slowly spiralled away northwards until it reached the point where the incoming tide pouring through the sound hit the Atlantic swell, creating standing waves some two metres high that felt distinctly unsafe. Unable to follow, I stared wistfully after the shark. The sea around me exploded with greater launce, baitfish that leapt from the water and pattered back like rain as mackerel hit them from below.

Facebook Twitter Pinterest ‘The strange creatures follow the Gulf Stream to our coasts in the summer’ ... A sunfish being cleaned by pennant coralfish. Photograph: Dave Fleetham/Getty Images/Perspectives

I had promised to take everyone in our party out in a double kayak to see the sharks, so over the two days when the weather was calm, I was on the water almost continuously. We saw perhaps a dozen, of which one stood out: a monster twice the length of the boat that looked almost as broad as a whale. The largest basking shark ever measured was 12 metres (40 feet) long, but the combination of hunting, bycatch and boat strikes nowadays makes it less likely that they will live long enough to reach that size. The beast we saw was probably about as big as they now get. The same feral ecstasy – a primal thrill mingled with an ancient recognition – returned every time.

The sharks were not all we saw. Twice, different fins emerged from the water: tall, slim and translucent, flopping from side to side. They belonged to sunfish: the strange creatures with almost circular bodies that follow the Gulf Stream to our coasts in the summer. The first one we approached was about a metre wide. It lay listlessly on its side, watching us with a vast, round eye. When I leant over to touch it, it flipped away with surprising speed and disappeared into the depths.

There is a call by ecologists for 30% of Britain's seas to be protected. How much have we achieved? So far, 0.01%

I would like to live in a world where such experiences are common. This is not an impossible dream. In the late 18th century, Oliver Goldsmith described the arrival of herring, as seen from the British shore. The fish, he recorded, were “divided into distinct columns of five or six miles in length and three or four broad; while the water before them curls up, as if forced out of its bed … the whole water seems alive, and is seen so black with them to a great distance that the number seems inexhaustible.” The herring were followed by massive cod, spurdog, tope and smooth hound, longfin and bluefin tuna, blue, porbeagle, thresher, mako and occasional great white sharks. Moving in behind, within sight of the shore, were pods of fin whales and sperm whales.

This astonishing congregation of life has all but gone, largely through overfishing. But marine ecosystems recover very quickly when they have the chance. The crucial policy is to decide that large areas should no longer be commercially exploited. There is a longstanding call by ocean ecologists for 30% of Britain’s seas to be protected. How much have we achieved? So far, 0.01%: tiny pockets of sea around Lundy island in the Bristol Channel, Lamlash Bay off the Isle of Arran and Flamborough Head in East Yorkshire. Everywhere else, commercial fishing is permitted to rip up ecosystems and suppress the recovery of our natural wonders.

Overfishing is as big a threat to humanity as it is to our oceans | Dermot O'Gorman Read more

It is madness, not least because one of the victims of this policy is the fishing industry. When you establish reserves in which fish and shellfish can breed and grow to large sizes, the “spillover effect” – fish migrating into the surrounding waters – greatly increases the total catch. Declaring areas of sea off-limits to the fishing industry would also revitalise other coastal industries, as divers, whale and dolphin watchers and sport fishers – all of whom tend to bring in more income and jobs than commercial fishing does – came to witness the astounding spectacles that would result.

This marine rewilding could make emotional experiences of the kind I now live for available to everyone. We owe it to ourselves, as well as to the other species with which we share the world, to allow the seas that surround us to regain their wild enchantments.

This article is part of the Guardian’s Wild supplement. To read the rest, pick up the newspaper on Saturday 4 February