It's early October but the midday sun is torrid. Beyond the scrubby hills the sea glitters like hot steel. Then suddenly, from a corner of our vision, we see him leaping through the dunes. Looking always behind him, he stumbles on tussocks, zigzagging wildly, a holdall in his hand. Our throats feel drier than the desert air. He is big. He looks very afraid. Welcome to Cape Gata - fortress Europe's front line.
The Spanish Mediterranean's last truly wild shore, the Cabo de Gata seems like another continent from the costas of the posters. We were on a three-day trek along the long-distance path from Carboneras to San Miguel; 60km via mountains, coves and beaches virtually unchanged since Phoenicians sailed by. Rain is rarer than gold dust here and nowhere in Europe is as seared by the sun, the heat guarding its secret more effectively than the Natural Park status conferred in 1987.
Carboneras, a small cement-making town-cum-aspiring resort, seems unlikely to feature on A Place in the Sun, despite 16km of often-empty beach. It's a bleached Andalucian fusion of Castleford and Cleethorpes. We feel sorry for the tourist boss. Even Saatchi & Saatchi would struggle with a name that translates as Coal Bunkers.
Finally tracking down a map, we embark without conviction until a glimpse of Agua Amarga - a pearl so rare and lovely I wince to advertise its name - magically reminds me why I planned the trip. Before a beached fishing boat, the tiny hotel with oasis-green garden and tree-shaded pool resembles a postcard of yesteryear Spain.
The Hostal Family, Michelle and René's French-run hotel, has for three generations remained as charming as the view. The delectable dinner of Andalucian-French-style dishes tugs at our heels as we sweat up the escarpment sheltering the bay the next morning.
The high plateau looks like Scottish moor sown with rosemary and thyme. The sun is Saharan but a morning sea breeze fuels our feet. There are cliffs, ochre hills, blue sea and cloudless sky: not another human being apparently in Spain. We soon learn the GR92 is more route than track - often mere fancy, sometimes a leap of faith.
San Pedro's Cove opens at our feet like an abyss to another world. Down a horrendous-looking scree, 300 metres vertically below, is a scene from an adventure book: a perfect half-moon bay, ruined castle on an outcrop and, in a forest of agaves, a splash of meadow green. Accessible only by precipitous paths, the cove was once a pirate sanctuary. In fact, it looks like paradise. The only snag is getting down.
The beach at first looks as untrodden as a Bounty bar ad; but then - scarcely lessening the impression - in an upturned boat's shade I spy a nymph-like trio of naked girls sunbathing. Clothed and bearing rucksacks, we feel a little out of place. A few male nudists emerge and glower at us. By the castle is a spring, the only fresh water in 50km, its trough built by 16th-century pirates. We munch our bocadillos placidly.
In the dusty 10km to former gold-mining town Rodalquilar we are scrutinised three times by Civil Guard patrols. Is it paranoia or are we being tracked? Are they observing or protecting us? During the next days, wherever 4x4s can penetrate the Guardia appear. Occasionally one waves.
Footsore and very thirsty, we look down from the heights at La Isleta del Moro. Contrary to expectations, it's not an island but a cluster of white cottages astride a rocky spur dividing the beach - possibly Spain's loveliest but loneliest bay.
At the Hostal Isleta fishermen's nets dry on the terrace where we sip a couple of cool beers. Our room is dingy, service grudging, but dinner is fresh sea bass landed at the hotel door. Life here has scarcely changed for centuries. Men repair nets; women launder in the wash house. Other amenities comprise a post box and small shop. In Spain's ultimate Mediterranean hideaway, even the sea looks too hot to bathe.
The route gets wilder, still more scenic. We find jewel-like coves with pristine-sand crescents that the park's constitution calls virgin beaches. Skirting El Fraille's 500m-peak ruined castles peer precariously from dizzying cliffs. There are prickly pears and cacti. And then comes a surprise.
San José from the cliffs looks like a time-share prospectus pasted upon the surface of Mars; the ranks of white houses, resplendent marina and palm-lined promenade are incongruous in this kiln of sun-scorched hills. Where the track ought to be is a descent over rocky outcrops between the new villas. Mostly deserted, their owners' provenance is uncertain, though some do have garden gnomes.
Beach-level, San José is a northern European's Spanish fantasy come true. It looks fresh; the original fishing village - official population still 175 - is somewhere under the cement. It has, we admit, a certain unreal charm - a sanitised south where you might safely bring children - but whatever is it doing in a desert natural park? At a promenade café, people stare at our backpacks as if we are aliens.
The make-believe enclave ends as it began; the contrast with reality, the scrub and dusty track, is like passing through an airlock into another world. The temperature seems to rocket 10 degrees. The dunes shimmer in the sun. Our thoughts are fixed on water. Then, like a frisson in the heat, our path crosses with the running man's. He sees us; sees the track; falls in casually behind us. Near the lovely Genoveses beach we are three isolated figures in a wild and empty landscape. We instinctively walk faster. He keeps up but does not gain. And suddenly I read his mind: cast alone into this wilderness he hopes we may lead him to civilisation. I imagine his panic: wherever he has struggled from, whatever he has paid, this is not his promised land.
Despondent or weary, as the track steepens he falls gradually behind. Glancing back I see him stop, double up and retch. I leave a half-bottle of water - hoping he finds it before the Guardia find him. They say that boatloads of illegal immigrants are dumped here but most are soon caught. In any direction it is far to his dream. When we finally risk pausing to drink, I feel irrationally guilty, inexplicably ashamed.
We have one last haul to the Cape Gata lighthouse before plunging to the isthmus between the sea and the lagoon. Narrow as a ribbon, its eight arrow-straight kilometres of searing metalled road make a testing finale to Spain's desert by the sea. Beautiful, dramatic, an experience like no other in Europe, for us perhaps its greatest pleasure is now having it behind us. The flamingo-splotched saltpans - famous since antiquity - scarcely get a second glance. All we want is a beer.
The nearest airport is in Almería, which is served by easyJet (0905 821 0905; www.easyJet.com) from Gatwick and Stansted, Ryanair (0871 246 0000; www.ryanair.com) from Stansted and Monarch Scheduled (08700 405040; www.flymonarch.com) from Birmingham and Manchester. To reduce the impact on the environment, you can buy an "offset" from Climate Care (01865 207 000; www.climatecare.org). The environmental cost of a return flight from London to Almería, in economy, is £2.70. The money is used to fund sustainable projects. Rail Europe (08708 371 371; www.raileurope.co.uk) offers routes to Almería via Paris and Madrid.
Hostal Family, Calle La Lomilla, Agua Amarga, Almería (00 34 950 138 014). Doubles start at €45 (£32), including breakfast. Hostal Isleta del Moro, Calle Mohamed Arraez 28, La Isleta del Moro, Nijar, Almería (00 34 950 389 713). Doubles start at €50 (£36), room only.
Hotels in San José are listed on the website: www.cabodegata-nijar.es
Cabo de Gata National Park (00 34 950 380 299; www.parquecabodegata.com).
Spanish Tourist Office: 08459 400180; www.tourspain.co.uk