I have never been so relieved to see a wooden beach house in my life. After six hours of driving from Billund airport, complete with a wrong turn that took us through what I can only describe as someone's beetroot field, we finally spotted Skastrup Strand. My partner was navigating using a phone that had decided Denmark was essentially one large roundabout, and I was doing that thing where you grip the steering wheel too hard and make cheerful comments about "seeing the real countryside."

The beetroot field was not the real countryside I had in mind. The farmer, who appeared from nowhere on a tractor the size of a bungalow, found it considerably funnier than we did. He waved us back toward the coast with the kind of hearty Danish laughter that transcends language barriers. We were, it turns out, exactly four miles from where we needed to be. Four miles of root vegetables.

But then the sea appeared, grey and glittering under a sky that couldn't quite decide what it wanted to do with itself, and there was our little holiday home, all timber cladding and generous windows looking out across the water. I had packed for British weather, which turned out to be excellent preparation for Danish weather in late September. This would become a recurring theme.

We dumped our bags with the enthusiasm of people who had spent too long in a hire car smelling faintly of previous occupants' sandwiches, and immediately decided on a walk. This was, in retrospect, optimistic. The path along Skastrup Strand stretches in both directions, sandy and scattered with the kind of smooth stones that Scandinavian beaches seem to produce effortlessly. We headed north, toward the headland visible in the distance, me in walking boots I had optimistically waterproofed back in March.

The rain started precisely seven minutes later. Not dramatic rain, not the sort that sends you sprinting for cover, but a steady, purposeful drizzle that somehow found its way through my supposedly waterproof jacket and into that specific spot between shoulder blades where discomfort lives. We persisted, because we are British and this is what we do. We walked past the scattered holiday homes, each one shuttered and peaceful, past the little wooden jetties where fishing boats bobbed, past a woman walking a dog that looked at us with the pity only a dry animal can muster.

The headland never got closer. This is the cruel geography of coastal walking, where distances stretch like pulled toffee. After forty minutes we admitted defeat and turned back, by which point the rain had graduated to something more assertive. We squelched home, passing the same dog walker going the other way, her expression unchanged, as if wet English tourists were a standard feature of the Danish shoreline.

The following morning brought that particular miracle of northern European weather, where yesterday's downpour becomes today's sparkling clarity. We set out again, this time south toward the marshlands behind the beach, where wooden boardwalks keep your feet above the boggy ground and birdwatching hides offer shelter when the next inevitable shower arrives. I am not a serious birdwatcher, but I am an enthusiastic shelterer, and the hides became my favourite discovery of the trip.

We developed a rhythm over the week. Morning walks in whatever conditions presented themselves, afternoons reading in the house's generous living space while weather systems passed overhead like slow-moving freight trains. One afternoon we walked fully eight kilometres along the beach, the tide retreating to expose sand flats where lugworms had left their decorative casts, the sky a vast moving canvas of grey and silver and occasional startling blue. Another day we managed perhaps twenty minutes before horizontal rain sent us retreating to the warmth of the wood-burning stove, where we sat in damp socks and felt genuinely pleased with ourselves for the attempt.

There is something peculiarly satisfying about walking in weather that doesn't quite cooperate. Perhaps it appeals to some inherited British instinct, the same impulse that sends people onto windy piers with ice creams. Or perhaps, as I found myself reflecting during one particularly soggy return journey, it simply makes the warm and dry afterwards feel earned rather than merely comfortable. The house at Skastrup Strand, with its underfloor heating and well-equipped kitchen and windows that framed the changing sea, became a sanctuary precisely because we kept venturing out into conditions that sent us hurrying back.

On our final morning, we walked north again, toward that same headland that had defeated us on arrival day. The weather held, just barely, clouds massing on the horizon but keeping their distance. We reached it this time, a modest elevation that nonetheless offered views across the belt of water toward smaller islands, the wind carrying that particular salt-and-seaweed freshness that makes coastal walking worthwhile regardless of meteorological circumstances. I stood there, slightly out of breath, aware that my waterproof trousers had finally given up somewhere around the knees, and felt something close to contentment.

The farmer in the beetroot field had been right to laugh. The wrong turn, the rain, the walks abandoned and walks completed, they were all part of the same slightly absurd adventure. We drove back to Billund with the car smelling now of damp wool and success, already arguing about whether we would return in spring, when the weather might be different, or whether the unpredictable Danish skies were precisely the point.