I should have known the holiday was going to be interesting when I missed the turning for Gilleleje entirely and found myself in a car park next to a fish smokery, wondering why my sat nav sounded so deeply disappointed in me. Three-point turn, a bit of muttering, and twenty minutes later I was crawling along Strandvejen with the sea flickering through the pine trees and my blood pressure slowly returning to normal.

The cottage at Gilleleje Strand sat tucked behind a low dune, weathered wood and white trim looking like it had been there since someone first thought "actually, the seaside isn't half bad." I dumped my bags with the enthusiasm of a man who had been driving since dawn and immediately went the wrong way down a sandy path that I was certain led to the beach. It did not. It led to a small clearing where someone had arranged driftwood into what I can only describe as a rustic dining set, complete with a table that wobbled if you breathed near it. I sat there anyway, ate a squashed sandwich from my glovebox, and decided this accidental discovery was absolutely the plan all along.

The next morning I set out with proper intentions, map in pocket and coffee in hand, to find the harbour. I found something better by simply not finding it. A narrow lane I took to avoid a cyclist led me past a garden where an elderly chap was tending tomatoes in a greenhouse made entirely of old windows. He waved. I waved back. We did not share a language beyond that, but he pointed me toward a gap in a hedge that I would have walked past a hundred times.

Through that gap was a small cove, barely twenty metres of pebbles, where a woman in wellingtons was collecting something from the rocks with a determined expression. She told me, in excellent English, that she was after bladderwrack for her garden, and that her grandmother had taught her which bits to take. I helped for ten minutes, badly, and left with a handful of something I later had to google and a sense that I had stumbled into a layer of Gilleleje that no brochure was going to show me.

Getting properly lost became my strategy after that. I abandoned the main beach, lovely as it was, and wandered the back paths where holiday cottages gave way to proper houses with proper gardens and cats that followed you hopefully for a hundred yards. I found a bench facing a field of rye, no view of the sea at all, where someone had left a paperback in Danish and a half-eaten packet of biscuits. I read neither the book nor ate the biscuits, but I sat there for an hour watching a red kite circle something invisible in the distance.

The real gem came on my third day, when I took a wrong turn returning from what I thought was a shortcut to the local shop. The path petered out into brambles, I swore creatively, and then I saw the chimney. A tiny brick cottage, almost swallowed by vegetation, with a hand-painted sign offering coffee on Saturdays. It was Wednesday, but the door was open and a woman was inside painting watercolours of fishing boats. She made me coffee anyway, refused payment, and told me her grandfather had built the place in 1923 as a summer retreat for his family from Copenhagen. She had retired here permanently fifteen years ago and now she painted and talked to lost strangers. I stayed two hours.

By the end of the week I had stopped trying to get anywhere in particular. The harbour, when I finally found it properly, was pleasant enough, all bustle and ice cream and the smell of fresh herring. But I kept thinking about that cove, that greenhouse, that impossible coffee cottage hidden in the brambles. I had arrived thinking I would tick off the sights and eat the famous fish and come home with photographs of sunsets. Instead I came home with sand in my shoes, scratches from brambles, and the certain knowledge that the best thing you can do in a place like Gilleleje Strand is to miss your turning and see what finds you instead.