You need a car, and you start by taking the only bridge south out of the capital. The first turning off to the right leads you to the beach at Caparica - and to everyone else in Lisbon who is not tied to home or office. But that doesn't matter, because Caparica is not one beach, but 20.There are family beaches, nudist beaches, noisily musical beaches, beaches for those who like bookish silence - and they're all linked by a little toy train that runs along the dunes.
The dunes themselves are topped by scores of picturesque shacks, each of which has its own fanciful aura. The local authority has been saying for years that it will sweep these pieces of folk-art off the map, but inertia has so far preserved them. The gaily coloured fishing boats with their rearing prows are not just for show: go down to the beach at midnight and you'll see them landing their catch of sardines and selling it on the spot.
The 20th beach, Fonte da Telha, seems to go on for ever, but that's because mile after mile is unpunctuated by landmarks: just cliffs, dunes, sand and sea. Actually there is a landmark, though this is for cognoscenti: a pool of blue mud, halfway up the cliff, which young Lisboans smear on their bodies and let dry in the sun. Very medicinal, they say.
Strike out on your own inland and you find a terrain which seems curiously outside time. You skirt Lake Albufeira, cut off from the sea by a spit of sand, and surrounded by gypsy encampments. You wind along a cliff-top road to Cabo Espichel, with its Miss Havisham of a church still beautiful beneath its layers of dust, and with its vast empty monastery. Beyond that you'll find the nature park of Arrbida - a place to dump the car and walk.
Then you find civilisation again, in the form of a fishing-port called Sesimbra. With its cobbled streets and fading wall-tiles, this stout little town can't have changed much since the Renaissance, and there's the ubiquitous whiff of the fish on which its economy still depends.
Nearby Setbal was a Roman fish-salting port, and if you visit the tourist bureau you will find yourself walking on a glass floor protecting one of the original factories. The old town is painted like a sweet; its pedestrian precinct is a great place to hang out under the streamers spanning its streets.
A ferry runs across the bay, and from it you see armies of giant jellyfish and big dolphins turning cartwheels simply for the hell of it. The ferry's goal is a long strip of land called Tria, once a Roman military base, now a string of beaches that get progressively wilder the further you go.
The landward side of Tria skirts a sea of carefully cultivated rice fields and mud flats: this is the Sado river estuary, where salt and shellfish have been staples for 3,000 years. The villages are all decorated in the same style, with a broad ultramarine band outlining every building. Each belfry and tower has a nest of storks. Continue south towards the Algarve, but don't make the mistake we did of heading for Sines. The old town may be pretty, but it's dwarfed by one of the biggest oil terminals in the world: from a distance it seems to be surrounded by motorways, which on closer inspection turn out to be shoals of giant pipelines. On the other hand, 10 miles south of Sines is a string of gorgeously unspoilt beaches, of which the best is Porto Covo. No music, and just one rough shack dispensing Coke and perfect fish salad for 75p.
We drove back to Lisbon by the inland route, where the country roads are excellent. This took us through cork country, where lorries are piled high with the stuff and the painted azulejos (tiles) on the railway stations show cork-harvesters at work. And here we passed through a succession of beautiful medieval towns - where we met no touristsn
You can fly to Lisbon from Heathrow on TAP Air Portugal (0171-828 0262) and British Airways (0345 222111); from Gatwick on AB Airlines (0345 464748); or from Manchester on Portugalia (0990 502048). For two people travelling together, the best deal for visiting the Costa Azul is an offer from TAP Air Portugal that begins on 1 September. If each person pays pounds 150.80 return (including tax) for the air fares, the airline throws in three days of car rental.
By train, Rail Europe (0990 300003) has fares from London to Lisbon for pounds 287 return. Passengers change trains at Paris and Hendaye.
Further information: Portuguese National Tourist Office, 22 Sackville Street, London W1X 1DE (0171-494 1441).