We are on the beach at Cayton Bay, south of Scarborough, listening to James Turner, the tutor from Scarborough Surf School: "This is the nose and this is the tail." He's talking about the surf board. "These are the rails ... " The sides in other words.

I love all the surf talk. I want to get good in surf talk. After all, it's a lifestyle, isn't it? A surf shop owner told me once that a customer bought a top-of-the-range board, then asked him to drill eight holes through it. He didn't want to go near the sea, just bolt it permanently to his car roof-rack.

I've a sneaking suspicion that I fall into this "lifestyle surfer" category. Last summer I wore a T-shirt that read "Enter the Realm". It was something to do with surfing, I knew that much, and it made me feel good. I was in the Realm. Except I wasn't. Now I'm in the realm. The greyish-brown North Sea, with a sharp wind bowling in from the Baltic. Can this really be the next big thing in British surfing?

"Yes," says James emphatically. "With modern suits, the cold is not an issue out here, and we've got some fantastic surf. I've had water five times as tall as me in some spots. Barrel-rolls that you could fit a van inside."

"And the less-than-turquoise water?"

"Clay deposits offshore," says James.

Scarborough has this knack of pulling off some astonishing moves when in economic need. In the 1600s it announced that the acidic waters running from under the cliff were a sovereign remedy for various ailments. The following century it introduced the novelty of bathing machines, and the arrival of the railway in 1841 triggered a tourist boom that lasted a century. Then in 1932, believe it or not, it briefly became the world capital of big game fishing, when bluefin tuna were discovered. Now, in the 21st century, it has discovered that it has some of the country's best surfing. It doesn't surprise me: having visited this coast during stormy weather, I know how vast the waves can get.

James shows us how to scoot a board over the relatively small incoming waves, then turn and get aboard, ready for action. The vital trick is in timing the moment that you leap to your feet, but James helpfully steadies the board, pushes and shouts, "Now!"

I'm astonished to find that I can stay on my feet for a whole second. A few more attempts and I stay up for several seconds. My son Niall, 13, does even better, only to be outdone by six-year-old Maddy, who stands up on her first attempt, and stays up. On an eight-foot board she looks like she's riding a barge. The sun comes out, the sea sparkles and for almost two hours we forget about the chilly water and are totally absorbed in our efforts.

"It really is a sport for all ages," says James when, after two hours, we finally head back to the hot showers, tired but elated. "We've even taught people in their late 60s."

In the warm shop, with a mug of tea in hand, he shows us some photos of big waves: cavernous tubes of water containing some crouching tiger of a surfer. These were not taken in Hawaii, he explains, but on the English east coast. I ask where precisely and he grins. "We call those places Secret Spots. People don't like to publicise them too much. Anyway they are extremely dangerous if you don't know what you are doing."

James does. Like many surfers up here, he travelled far and wide before finally waking up to the fact that his own backyard was pretty good too.

Down in Scarborough town, at another surf shop, Fluid Concept, Steve Crawford tells the same tale: "I come from Scarborough, but I always accepted that Cornwall was the best. I lived there for years before I came back and explored this coast. It was then I realised we had some very special surf."

Steve takes us out to try paddleboarding – this is done on a large surfboard, and you propel yourself using a long-handled paddle. "It's very different from normal surfing," he says. "You have more time to look around and enjoy the seascape. People take their lunch, go fishing, make a day of exploring the coast."

Scarborough itself is really two bays: north and south, separated by a crag topped with a castle. The steep streets and harbour give it the feel of a fishing village, but there's Victorian grandeur at the edges, and seaside postcard trash too. In a day you can get through quite a spectrum of entertainment here: go surfing in the morning (after a call to the surf shop to check which bay is best), lunch on local seafood, ride the dodgems and the big wheel in the afternoon, then head for the internationally renowned Stephen Joseph Theatre to catch a play in the evening.

We stroll along the promenade, admiring the usual weekend quota of Harley Davidsons and discover the Tunny Club, once the haunt of a select band of big game fishermen that included Baron Rothschild and, it's claimed, Errol Flynn. It's now an excellent fish and chip restaurant, and its walls are adorned with photographs from the improbable heyday of the North Sea tuna, in the 30s.

It is a salutary reminder of how productive the North Sea once was. In his book An Unnatural History of the Seas, Professor Callum Roberts of York University paints a picture of a sea that brimmed with life until the arrival of the steam trawler: shoals of haddock three miles long, oyster beds as wide as Wales, salmon fisheries filled with wild salmon rather than lice-infested chemically stained Franken-fish. The North Sea used to be a world-class marine paradise. And there are those who believe such splendour could return, if and when the government gets round to establishing the long-awaited marine reserves.

"We've lost 98% of the original biomass of the North Sea," says Rob Stoneman of the Yorkshire Wildlife Trust. "Bottom trawling has been an unmitigated disaster. But there is a chance that we can rejuvenate things – bring back some of the world's richest fishing grounds, and maybe even some of the great megafauna we once had: the sharks, turtles, dolphins and so on."

We move on, from the noise and excitement of South Bay to the quieter North Bay. In late Victorian times this area was the site of some ambitious schemes: a giant outdoor theatre, and a mile-long railway to carry visitors around the bay. The 3,000-seat amphitheatre is awaiting refurbishment, but the railway still runs, with original locomotives, providing a handy way to reach the Sea Life Centre (and one of Scarborough's best restaurants, the Glasshouse Bistro). Dominating the bay these days is The Sands, a £155m redevelopment of a 30s water park and entertainment complex. For now there are some spectacular sea view apartments and a surfers' bar, Blue Crush, but a modernised water park is to follow.

Despite all the new-builds and revamps, it is the sea that surfers see as the key to Scarborough's long-term future. Some have been active with anti-pollution campaigns, others with attempts to establish marine reserves.

"The North Sea has this image of a poisoned cold waste," says Steve Crawford in his surf shop. "But it has a lot to offer, especially if we start taking care of it. That is something surfers have realised."

As if to confirm Steve's optimism, the sea gives us a sign. We are walking along Marine Drive, the road that loops around the headland between the town's two bays. Niall spots something in the water and we all stare in astonishment as a pod of porpoises cruise by, just 50m off shore.

"I'll paddleboard round here tomorrow," says Steve. "I reckon this area is a nursery for porpoises. If we can prove it, we can try and get it protected."

It is a magical moment and, as if to remind us where we are, our natural history reverie is disturbed by the raucous shouts and screams from the dodgem rides on the harbour wall. The porpoises don't seem bothered, however, and carry on rolling through the swell until they pass out of sight.

• Fluid Concept (01723 354263) in South Bay, Scarborough, hires paddleboards at £10 an hour. Two hours' hire of surfboard, wetsuit and boots is £14. Steve Crawford organizes beach clean-ups and other activities for Surfers Against Sewage (sas.org.uk). Scarborough Surf School (01723 585585) offers two-hour surfing lessons for £25. Self-catering flats at The Sands in North Bay cost from £145 for a summer weekend (01924 251375). More information on the area from: yorkshiremoorsandcoast.com, and the Yorkshire Wildlife Trust, ywt.org.uk.