Christmas dinner for Kate Moss and friends was in the diary long ago. Earlier this month he rustled up something for Gwyneth Paltrow and Chris Martin in the Hamptons. But in between, private chef Kevin Mikailian was preparing food for a rather different clientele.

Working in an abandoned warehouse on the outskirts of Calais, he was in his chef whites standing over huge, bubbling cauldrons of dal readied for the migrants and refugees who have found themselves in the place that’s been called the biggest slum in Europe: the so-called Jungle of Calais.

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Mikailian was presiding over a team of people, most of them young, most of them having “never spent a day in the kitchen”. Between them, they were aiming to produce up to 1,500 hot, nutritious meals that could be ferried the short distance to the camp. None of them had done anything like this before.

Elsewhere in the warehouse it was the same story. People were sorting black bin bags full of clothes into cardboard boxes labelled Fleece Male (medium) or Small Long-Sleeved Tops. Some of those doing the sorting had only arrived in Calais the previous day.

The woman showing me round, Philli Boyle, had no prior experience in the field of aid or emergency response. She and a few friends had simply seen the same pictures as everyone else, believed someone had to do something and put out feelers on Facebook. Now she’s been in Calais for months and has found herself at the heart of what looks like a disaster relief operation.

This is one of the stranger aspects of the humanitarian sore festering 22 miles from the coast of England. The Jungle is as bad as any slum or shantytown you might find in what used to be called the third world – except it’s here in the first world, in the heart of Europe. Up to 6,000 people are living on a patch of wasteland, much of it contaminated with human faeces, with no infrastructure whatsoever. No roads, no sanitation, no power except that supplied by humming generators.

Peek inside a tent so flimsy it would struggle to cope with a couple of nights at a music festival, one pitched on sinking mud, and you discover that this is home in midwinter to four adult men. In great demand are the timber frames covered in tarpaulin that form a structure smaller than the average garden shed. Six men sleep inside one of these.

No one can wash properly, because there are so few water points. I saw men washing their feet, but unable to keep them clean: the ground around the tap had turned to mud or else was clogged with garbage. Meanwhile, a girl – seven years old at most – was rolling a plastic water barrel towards the tap, presumably to fill up and supply her family. There are 60 showers for 6,000 people.

Fury cannot be the only response to the camp. Admiration is the right reaction too

All of this is happening and – this is what’s so strange – there is nobody in charge. If this had been a conventional disaster, the United Nations would have come in and then the big aid agencies would have got busy. But this is Europe, which is meant to be beyond the need of such help. So the UN and UNHCR are not in Calais, while there’s little sign of Oxfam, Save the Children or the Red Cross. That’s not because they don’t care: aid workers tell visiting politicians they feel they have no mandate to operate in Europe (though Médecins Sans Frontières is there, its first such operation on French soil).

As for the French and British governments, their only presence comes in the form of uniformed security personnel policing the barbed wire perimeter, watching – but not helping – the people within, tasked with preventing them breaking out and heading for the tunnel or sea that might take them to England.

The camp has been left instead to the volunteers. That big warehouse – with its kitchen, its clothes-sorting operation and its workshop where carpenters, some professional, some amateur, churn out timber frames for shelters as fast as they can construct them – has been set up by a small, Calais charity, L’Auberge des Migrants. It has grown tenfold in three months, helped by the ad hoc efforts of assorted British groups.

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The result is that, for the outsider, the atmosphere can seem to be part refugee camp, part Glastonbury. Threading their way around the muddy paths and dirt tracks are countless young Brits, dreadlocked and nose-studded, friendly and eager. Some are there to teach English in the pop-up classroom. Some are helping out at the library (announced by the sign that says “Jungle Books”). Some are on hand in the large, domed tent set up by two young British playwrights that serves as a kind of arts centre. Musicians from Syria, Iraq or Afghanistan sit in a circle and play songs from the old country. On the walls are drawings or photographs made by refugees. One shows a tree-fringed lake, covered in morning mist. The caption says, “Sometimes I come here and stand for a few minutes, imagining that this is what England looks like.”

Judged by the usual standards of policy, this is awful. Both the French and UK governments are guilty of an appalling abdication of responsibility, insisting that the Calais camp is not their problem and so turning their backs on it. They won’t supply it with the basics necessary for human existence, lest they be seen to legitimise or entrench it. This is a shameful response, putting politics before fundamental human decency.

And yet fury cannot be the only response to the camp. Admiration is the right reaction too. First for the migrants and refugees themselves, for their resilience and dignity – for the ingenuity that has seen them build a high street full of chipboard restaurants and plywood cafes, as well as mosques and at least one church.

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But it’s impossible not to admire the volunteers too. For no pay, they have given up comfortable lives to build or cook or teach, to provide for people they have never met because they know that, if they don’t, no one else will. Some are young or retired, with time on their hands. Others have put busy jobs or careers on hold. But none of them had to trade comfortable lives for working in the mud and squalor of the Jungle. No one forced them to rent a van, fill it with tarpaulins or bulk packs of rice and take it across the Channel. They did it simply because they were moved by the sight of their fellow human beings in distress.

And this is what sets them apart from the governments that claim to represent them. The volunteers saw in the faces of those refugees not a problem to be addressed – or, more accurately, avoided – but people just like them. The same is true of all those who have given, and are still giving, to the Guardian’s unprecedentedly successful Christmas appeal.

Within a few hours of the Paris attacks, someone tweeted the advice they’d learned from Fred Rogers, the long-serving face of American children’s television. Don’t look at the killers. Look for the helpers. In what has often been a harsh, dark year, this ragtag, impromptu army of volunteers has been a point of light. They are the very best of us.