They say in Mexico City that the pigeons drop dead from the sky when they hit the smog. Aldous Huxley once said he had never felt so bad tempered as he did during a week’s stay there.

Can it be that bad? Our taxi driver guide immediately takes the matter into his own hands and, ignoring red traffic lights, drives us in his yellow VW Beetle beyond the polluted city to Teotihuacan, the first great civilisation of central Mexico, which existed between AD 100 and 600. We haven’t had a chance yet to change money and so, with a smile as big as the nearby Pyramid of the Sun, the driver pulls down his socks, pulls out his cash and gives us some to be going on with. The site of Teotihuacan is sublime – with vast pyramids, plazas, esplanades and Aztec ruins. Back in Mexico City, we dine at Prendes, where Leon Trotsky and painter Frida Kahlo ate before us. Before eating, the maitre d’ thinks we should watch the game of jai-alai (pelota) being played next door with what looks like a giant banana. Gentlemen must wear a tie to watch the game and my companion is not wearing one. The maitre d’ takes his off and ties it round my friend’s neck, though he doesn’t give us any cash from his socks. The next day a policeman offers to drive us to the market in his police car, but doesn’t give us his tie either. We go to see the National Palace with its moving murals by founder of the Mexican muralist movement Diego Rivera portraying five centuries of Mexico’s history; the impressive Metropolitan Cathedral made of 3,000 tonnes of marble and granite; and the Museum of Anthropology, with its pre-Hispanic exhibits and remarkable design.

Later we visit Frida Kahlo’s house (a museum) but the man at the door says he’s taken all the pictures and furniture away and doesn’t let us in. So we go to the house where Trotsky spent his last years writing and tending his pet rabbit before he met an untimely end with an ice pick plunged into his head. The body has gone, but pictures and furniture are intact. Nearly 350 miles to the south is the graceful colonial city of Oaxaca, where the Mexicans say there are 20 earthquakes a day. The buildings are made of very chunky stones to avoid their effects. We stay in one such, the Hotel Stouffer Presidente, a heavenly former jail and 16th century convent. Nuns were banned in the anti-clerical 1860s and the hotel now has a sombre elegance, a swimming pool among the cloisters and attentive service. We feast on fried tortillas with chicharon, stuffed tamales, rolled tortillas with chocolate-based mole sauce and chicken, Tasajo beef and marinated pork with refried beans. Afterwards we sit at a sidewalk cafe in the plaza surrounded by Spanish baroque buildings and huge trees. Oaxaca has a famous twice-weekly market where ladies scrub their squealing piglets with washing-up liquid and women with flashing smiles and bright costumes sit amid the colourful riot of cardamom, pumpkin roasted in honey, papaya and glistening vegetables grown in the volcanic soil. They sell scarves woven in turquoise, pink and yellow, natural black earthenware, ponchos, green pottery and rugs that have taken two months to weave and tell the story of village life. A lady insisted that my friend ate chapulines – tiny red grasshoppers deep-fried in garlic-flavoured oil – from her brimming basket of dead and salty bugs.

We continued to Villahermosa and made an 80-mile jeep ride to Palenque, most sacred of Mayan ruins. Set in a parrot-filled, threatened rainforest, they rise on artificial terraces. Among them is the royal palace, with a tower which was possibly an observatory and a pyramid containing a royal tomb. Light in style, delicately embellished and with mysterious stone sculptures and glyphs, the place has a haunting feel.

Next stop is San Cristobal de las Casas, a little hill town 177 kilometres from Palenque. It was founded by the Andalucians in the 16th century. Indians in bright shawls drink hot chocolate and barbecue corn on the cob (served with chili) amid colonial mansions and Baroque churches. Across the border is Guatemala, with weather that the tourist authorities describe as eternal spring and a saint called Maximon whose favourite offerings are cigarettes and rum. We drive through the spectacular scenery of the Maya Highlands, 90 miles from Guatemala City to Chichicastenango, known, for obvious reasons, as Chichi. It is a very Indian town with cobbled streets and whitewashed houses and a Sunday market full of over-zealous traders selling dance masks and brand new ‘antique’ artifacts. We sit on the steps outside Santo Tomas church (16th century and built on the site of a Maya pyramid) amid the incense burning and flower sellers. Inside is the sound of praying. Our eight-year-old, self-styled guide, Tomas, points out that the rose petal and pine needle offerings are ‘pagan ritual, Mister’, but can’t answer any questions. It takes a while to twig he has simply learned his English tour script by heart.

He also takes us past a room filled with 50 young boys and shielded from the street by tarpaulin. Inside, all the Tomases of the town are glued to a television set, watching a Spanish-dubbed western.

We stay in The Mayan Inn with its open fires in bedrooms filled with Colonial chests, figures, carved furniture, antique mirrors and old Spanish chairs that the owner, Mr Clark, sometimes bought from earthquake victims in Antigua. There are no locks on the doors and attendants in local costume stand watch outside. In the courtyard a parrot sits next to an ancient Maya sculpture and a marimba band plays.

Lake Atitlan is our next stop: the romantic Hotel Atitlan overlooking the deep green lake and what appear to be most of Guatemala’s 33 volcanoes. Well, three, actually.

Next door are two partly built skyscrapers where work stopped more than 10 years ago when the Nicaraguan money from the Somoza regime dried up. We take a boat across the lake to the village of Santiago Atitlan, where local Indians throng around a man in the market selling PMT tablets as a cure for arthritis, old age, impotence and tiredness. This is also the home of the smoking and drinking Saint Maximon and of some atrocious military killings. I still dream of Guatemala City, crumbling Antigua, volcanoes, colonial charm and jungle. Of vivid fabrics, mountain regions, Mayan sites and marimba music. But not of poisoned pigeons . . .

How: This holiday was organised through Cathy Matos Mexican Tours (61 High Street, Barnet EN5 5UR; 081 440 4306) with flights to Miami with Virgin Atlantic and onward by AeroMexico. The firm could arrange an itinerary similar to that followed by Caroline Phillips from around £1,200.