Herons swoop over a flat-bottomed boat navigating a canal and rest in one of the water-loving ahuehuete trees on the embankment. In a nearby field, an ageing farmer with a straw hat and chiselled features checks his cabbages while two younger men weed a field of lettuces. Another man skilfully manoeuvres a wheelbarrow across a narrower canal and disappears past a bush of the white, trumpet-shaped alcatraz lilies that Diego Rivera was so fond of painting.

Welcome to San Gregorio Atlapulco – a bucolic paradise in the middle of the watery corridor along the south-eastern edge of the Mexican capital and one of the last true redoubts of the floating gardens, known as chinampas, that once sustained the great Aztec capital Tenochtitlan. But even here, where the madding crowd is still relatively far away, there is a palpable sense that the clock is ticking for this way of life.

"When I was a child, all the chinampas were cultivated all of the time. Now it is probably down to about a third," says Mario Medina, a 60-year-old chinampero who says his land has been in his family since time immemorial, but none of his five children have any intention of farming it. "I'm lucky if I get them to help for an hour. They are city people now."

These flat and fertile gardens, built from piles of mud anchored by the ahuehuetes, were producing multiple yearly harvests of crops such as tomatoes and courgettes long before the Aztecs arrived in the lake-filled valley in the 14th century. The chinampas boomed as the Aztec empire and its capital – also built on an artificial island – flourished. Their slow decline began once the Spanish conquest brought a new urban ethos that sought to dominate the wet environment, rather than working in harmony with it. But the real danger of annihilation only emerged hundreds of years later when Mexico City's population exploded.

With the mancha urbana – the urban stain – eating into chinampa territory in the south, a ban on construction on the islands towards the end of the 20th century helped slow the process. But incremental building continued, as did the chaotic urbanisation that both depletes and contaminates water in the canals. This encourages farmers to stop cultivating their land and build on it instead.

The veteran environmental journalist Ivan Restrepo applauds some new government farming incentives but says these are insufficient to avert the "unforgivable loss of the last remaining legacy of the impressive pre-Hispanic environmental tradition".

The most sensitive frontline of urban encroachment into the chinampas at the moment is Tlahuac, where some locals see the arrival of a new metro line as the beginning of the end. The new Gold line, due to open this spring, fills a gaping hole in the city's transportation network for existing residents along the route. But it will also make the semi-rural areas beyond much more attractive to migrants looking to set up a home within reach of city employment.

Taking a break from tending to his radishes on his Tlahuac chinampa, 72-year-old Sabino Martínez remembers the days when it was possible to drink the water from the canal, which is now flecked with rubbish.

Martínez's land has a view of the new metro terminal and some hills further south that he says were covered in cornfields not so long ago.

Now, he predicts, they will soon be covered in houses, leaving the chinampas as a shrinking island between the two. "It was once very beautiful here, but those days will never return," he says. "Now we are going to become just another part of the metropolis."