I should have known the holiday was going to be characterful when I got my first Danish lesson from a petrol pump attendant somewhere past Kolding. I'd stopped for fuel and a wee, and somehow managed to lock my keys in the boot while trying to retrieve my jacket. The attendant, a chap called Henrik with eyebrows like two caterpillars having an argument, watched me panic for a solid minute before sauntering over.

"First time in Jutland?" he asked, already knowing the answer. He had the spare key out of a magnetic box under the wheel arch before I'd even remembered hiding it there. "You English always hide them in the same place. We have a betting pool." I couldn't tell if he was joking. I still can't.

The drive to Flovt Strand proper took me through flat farmland and little clusters of red-roofed houses that looked like they'd been arranged by a tidy-minded child. I arrived at the holiday home complex in that particular late-afternoon light that makes everything look slightly apologetic. The key was in a lockbox, which I opened successfully this time, feeling disproportionately proud of myself.

My neighbour introduced himself within four minutes. Arne was seventy-ish, wearing sandals with socks in what I initially thought was irony, and was burning something on a disposable barbecue with the confidence of a man who'd never once produced edible food. "You are the English," he announced, rather than asked. "I am practising my English on you. It is not good, but it is enthusiastic." This proved accurate. Over the next hour, as his sausages turned to carbon, he told me about his wife's knee replacement, his grandson's suspicious girlfriend, and his theory that British people secretly enjoy terrible weather because it gives us something to discuss. "You are here for conversation," he said, poking his incinerated dinner. "The beach is secondary."

He wasn't wrong, as it turned out. The next morning I walked down to the shoreline, a proper Baltic beach with pale sand and that particular stillness you get when the sea is being polite rather than dramatic. An older woman was swimming in a floral cap, emerging to tell me she'd been doing this since 1987 and had "the circulation of a much younger seal." Her name was Birgit, and she lived in a house she'd built with her late husband, who had been "good with concrete, bad with compliments." She made me hold her towel while she did another length, then insisted I come for coffee because "you look like someone who needs feeding."

Her kitchen was overwhelmingly yellow. The coffee was strong enough to stand a spoon in, and the biscuits were homemade and slightly burnt, which I mentioned politely. "My husband said that for thirty-two years," she said, not sadly. "Now I burn them on purpose. It is my tribute." She showed me photographs of grandchildren, of the house being built, of a dog that had died in 2003 but remained, she said, "still present in the way the door creaks."

That evening, Arne reappeared with two beers and a bag of supermarket meatballs he'd finally accepted required oven-based preparation. We sat on my little terrace as the light stretched out, and he told me about working in a fish processing plant in Esbjerg for decades, about the peculiar pride of handling something that would travel across Europe. "The fish see more of the world than I do," he said, then laughed at himself. "This is not sad. This is practical."

A woman called Inge passed by walking a dachshund with the self-importance of a much larger animal. She and Arne had some rapid Danish exchange that ended with her laughing and me being none the wiser. "She says you have the face of a man who would talk to strangers," Arne translated. "This is her highest compliment."

I realised, somewhere between my third beer and Arne's second attempt at explaining Danish municipal governance, that I'd spent my first full day barely leaving the immediate area, and couldn't have been happier about it. The beach was there, patient and present. The characters were the destination. I came for South Jutland's coastline and found instead its coastline's inhabitants, who seemed to have collectively decided that any visitor needed proper induction through conversation, slightly flawed food, and gentle observation about their national character.

Birgit appeared the next morning with more burnt biscuits and a borrowed book of Danish short stories, translated, "so you can understand our darkness." Arne waved from his terrace, already burning something new. The dachshund passed again, acknowledging me with a snort.

I never did learn much about the broader area. I learned that Henrik probably wasn't joking about the betting pool, that Arne's sandals were genuinely just comfortable, that Birgit's yellow kitchen had been her husband's choice and she'd never changed it because "grief is not in the colour, it is in the removing." I learned that a holiday can be measured in conversations rather than kilometres, and that South Jutland, flat and unassuming and full of people who treat strangers as interruptions worth savouring, had given me exactly the break I didn't know I needed.

The sausages, I should note, never improved.