When I told my 10-year-old son Ben that I had booked a holiday in an isolated cottage without electricity, so there would be no TV and not much heating, he said, simply, "No." And he just repeated it whenever the subject came up – "No" – as though it was not only an unappealing prospect but actually impossible.

Nev, his father, responded in much the same way. Oh they'll come round, I thought – but the morning of departure has arrived and they haven't. "Surely you're looking forward to it a bit?" I ask a gloomy Neville. "Look, I've said from the start this is a terrible idea," he says.

Oh dear. Could he be right? Are we going to spend four days freezing, with the children endlessly tugging at our sleeves moaning that they're bored? At least Francesca, six, is enthusiastic. She sparked the idea by deciding one evening that we should go back in time, and turn off the TV and light candles. How lovely, I thought – let's do it properly …

We queue with the bank holiday traffic for the Isle of Wight ferry and head west across the island, gradually shrugging off the crowds. We pick up a key and unlock a gate and turn off on to a track that climbs upwards through heathland until we are looking over the sea. And there, hidden in the trees, entirely alone, is Longstone Cottage.

Built in 1900 for the estate's gamekeeper, our home for the next four days is a red-brick double-fronted Edwardian house, named for the Neolithic longstone on the brow of the hill. The first thing that strikes me as I walk in is the silence. It is amazing how much noise electricity makes: here there is no fridge buzzing. And of course there's no traffic.

I stand for a long time at the front door, staring at the view, at the valley stretching out in front of me, at the cows in the field. There's no other building in sight. And it is incredible, but all the stress and pollution of a long winter in the city – the dog shit and hard work and drum'n'bass spewing out of windows – just starts to fall away. Francesca is digging out a molehill, Ben is kicking a football around the garden, and Nev is banging around inside. Everyone is happy, just like that. It feels like an overwhelming testament to the power of environment.

Don't imagine Withnail and I. This is a National Trust cottage, which implies certain standards. The decor is neutral and tasteful. There is a small gas fridge, a gas cooker, and a combi boiler, so hot water on demand. There is no central heating and no heating at all upstairs, but there is a wood-burning stove in the sitting room and gas fires in the bathroom and dining room, though we never get the last of these to work. The house is cold – colder than outdoors – but we light the stove and make the living room our base.

After supper outside, we settle around the fire and read, which, I realise, is something we have never done before as a family. Isn't that sad? I think it is. I've never really thought of us as a family dominated by technology. I put restrictions on the children's viewing and computer time, and I barely watch TV at all. But the truth is that at home at this time, the children would be huddled by the telly while Nev and I grab a moment to catch up after work, and later Nev would be channel-hopping while I mindlessly flick around the internet or read beside him.

As the evening draws in we go round the house lighting the gas lamps – a gentle ritual that leaves the cottage glowing. Later the children have their first experience of being tucked up in bed with a hot water bottle. We all sleep for 11 hours.

In the morning we head for the beach. The west is the quiet side of the Isle of Wight. Not isolated – there are bustling villages packed with "great housing stock": picture-postcard thatched cottages and Victorian and Edwardian villas, evidence of the island's fashionable days when the likes of Tennyson and Dickens lived here. But this is rambling – not holiday park – territory, and much of the land is owned by the National Trust.

We head for one of their beaches – the sandy expanse of Compton Bay, accessed from the north by steep wooden steps. Out of the wind, under the cliffs, we expose our pale bodies to the spring sun. The children disappear for hours, running back and forth into the shallows and, in time-honoured tradition of this beach, modelling figures from the clay in the cliffs, before leaving them to bake in the sun.

Later, the silence of the night is broken – by music. Not exactly a rave, though – rather the distant wheeze of an accordion … In fact we have had advance warning of this and through the gloom we make out a troupe of morris dancers, celebrating the dawning of May Day by the Longstone. We leave the curtains open and watch them for a while before we go back to sleep. "Makes a change from gangsta rap," quips Nev.

Things bubble up in all this silence and space. I am sitting in the garden when Ben wanders up and asks me how much money I have, which turns into a conversation about what he's going to do when he grows up. Francesca has a nightmare that draws out her own anxieties.

Yet both of them – all of us – are so relaxed. And not just more relaxed than at home – more relaxed than we were last weekend, in a caravan. It's like a thermostat has been turned right down. Neither of them has said they're bored once. They keep finding new activities, or just wander round dreaming. Nev and I even get to lie in. I thought this would be the great sacrifice of having no TV but the children have started a mammoth game of Monopoly. And they're both being spookily sweet and polite, to us as well as each other.

They don't even moan when I suggest a hike. This area is some of the best-walked land in the UK, and for good reason. A network of walking and cycling routes zigzags across the island. The National Trust encourages roaming on the Mottistone estate, which the cottage sits on, so we climb through beautiful primrose woods and over heathland up to Mottistone Down.

Then off for Sunday lunch at the Crown Inn in Shorwell, which comes with a personal recommendation for decent food and being good for children – which it exceeds, having a trout brook as well as a playground. It's a warm, shambling place where yachting types rub shoulders with tattooed bikers, and ancient locals have tables reserved on this bank holiday weekend, their dogs resting by their feet.

Afterwards we all just want to go back to the cottage, where we while away the afternoon and our last evening. I can't resist my moment of triumph. "See?" I say. "We've had a good time, haven't we? Even Ben hasn't missed the telly."

"Yes I have," he says.

Oh well, shame I've booked for next year, then …

• Longstone Cottage (0844 8002070, nationaltrustcottages.co.uk) sleeps six, and costs from £372-£999 per week. From 18 November the gas lights will be replaced with electric wall lighting. The National Trust has another remote gas-lit cottage with no electricity in the foothills of Snowdonia, Foel Gopyn, which sleeps four, and costs from £346-£707 for a week. Red Funnel (redfunnel.co.uk) operates an hourly vehicle ferry crossing between Southampton and East Cowes, with return fares from £44. The Crown Inn (crowninnshorwell.co.uk) has main dishes from £8.95