By David Willey
BBC News, Naples
The EU is watching how Naples deals with the crisis
There is a sense of desperation in Naples, a teeming Mediterranean metropolis of nearly four million.
They have run out of landfills - usually former quarries - traditionally used to dump their rubbish. And they have failed to implement orders from Rome and Brussels to sort their waste for recycling.
The European Commission's deadline for Naples to solve its rubbish problem expired on Thursday.
Many families do not know which way to turn to keep their children healthy. Some have even requested political asylum in Switzerland as a last resort. So far, the Swiss have not been very responsive.
Naples - with its stupendous bay and harbour - was once a popular winter tourist destination because of its mild climate.
In February, its hotels are practically empty. Tour operators are worried about the appalling image of the city projected internationally by the rubbish crisis.
More than 250,000 tons of stinking, putrefying household waste lies uncollected along the streets of many of the outlying areas of the city.
Thousands of acres of land are filled with mountainous stacks of "ecoballs" - unsorted compressed rubbish, in which toxic waste is often mixed with ordinary household refuse and the remains of old cars.
Municipal workers gave up rubbish collections in December, and although the city centre has now been cleaned up and had most of its waste removed with the help of the army, the emergency continues. Firemen answer an average of 20 calls each night as blazes of rubbish light up the countryside.
From the military headquarters where he has taken up residence since being appointed Naples' "rubbish tsar" in January, Giovanni Di Gennaro surveys the very limited progress he has made.
"I have to get waste disposal moving again. I have been given until 7 May, before the hot weather arrives," the former chief of Italy's national police says.
"But Naples is still creating rubbish faster than it can dispose of it," he adds.
This week, he has been meeting with the Cardinal Archbishop of Naples to try to get the Catholic Church involved.
Dr Laghi argues that incineration is not a solution
One-tenth of the city's 281 parish priests are already giving lessons to their parishioners on how to sort their rubbish into different containers for plastic, paper, glass and compost.
The trouble is that most households in this sprawling city have never seen on their streets any of the new coloured plastic rubbish bins now common in other parts of Italy.
Luigi Berghantino, a postgraduate student, is a member of a group of concerned citizens - doctors, ecologists, physicists, judges, geologists, journalists - who monitor the waste crisis by holding regular weekly meetings in their spare time.
He seems satisfied by some of the decisions taken by Commissioner Di Gennaro.
"Di Gennaro has stopped the reopening of old landfills," Luigi says.
"He has created some new temporary storage facilities for waste, and he has understood that it is cheaper and more efficient to cart away Naples' waste by ship rather than by freight train to Germany as at present."
Ferdinando Laghi, another member of the group, is a hospital doctor who specialises in environmental medicine.
"Waste disposal here has run out of control, with illegal dumps being created and rubbish being left by the side of the road," Dr Laghi says.
"Incineration is not a solution, it neither disposes of the waste, nor does it remove the health hazards. It simply creates toxic dust and ash and attacks people's health in another way."
Last weekend, I joined thousands of families gathered in the Piazza Dante, in the centre of Naples, to hear TV comedian-turned-political-activist Beppe Grillo address a Refuse Day rock concert.
Edoardo Bennato was one of the star performers at the concert
There was loud applause for Mr Grillo's appeal to Neapolitans to declare their independence - just like Kosovo - in protest at the failure of both local government and the authorities in Rome to resolve the crisis.
Mr Grillo's blog - which mercilessly lampoons and mocks Italy's leading politicians - is the eighth most visited internet site in Italy, he claims. In a recent blog, he appealed to Germany kindly to invade Italy immediately to set things in order.
Dr Antonio Marfella, hospital oncologist, also joined in Mr Grillo's protest meeting.
The rubbish crisis has been out of control for at least 15 years, he told me.
"Big business all over Italy has profited by paying the Camorra, local organised crime, at extremely low cost, to dispose of their industrial waste by dumping it in the Naples area.
"Unfortunately the Camorra chose one of the most fertile and agriculturally profitable parts of Italy; it's as if they had chosen to dump toxic waste in the area where Champagne is produced in France," Dr Marfella says.
Edoardo Bennato, a popular Neapolitan song writer and rock star from the 1980s, was one of the lead performers at Mr Grillo's 12-hour marathon concert.
Anna says toxins are now affecting water supply in the city
"We love Beppe Grillo because he's outside the political system," Mr Bennato says.
"Italy is still not a real nation. It is a question of latitude, the difference between northern and southern mentalities. We have two different mentalities but only one nation, and it just doesn't work. This is what my songs are about," he says.
Anna Fava, a university student doing research into EU funding, blames local politicians - as well as organised crime - for the current mess in Naples.
"The political parties here are not real representatives of ordinary voters. They have bowed to big business and the Camorra and have connived at the mixing up of household and toxic waste. Now toxins are beginning to affect our water supply and the food chain," she says.