YOU’VE gone on a two-week guided tour of Egypt, and now you’re in Cairo. This morning, you went to the Egyptian Museum and peered at Tutankhamun’s funerary mask in a densely sweating crowd. This afternoon, you’re in a coach coming back from the Pyramids.

Your fellow tourists are full of complaints about the lewd liberties taken by the camel-drivers, you’re laden down with tawdry purchases, and the coach is stuck in traffic on one of the flyovers that cut through central Cairo. You look out, and in the middle of the expanse of biscuit-dry roofs is an extraordinary thing: a delicate stone pinnacle, carved into elaborate, fantastic forms. A little farther away, another and another; a dome rippling with lace-like arabesques

The coach moves on and the disloyal thought occurs to you: why aren’t we looking at that? But you’re flying to Luxor tomorrow and there won’t be time.

It’s a great oddity. Millions of tourists go to Cairo, and almost all of them take the same route, visiting only the ancient relics at Giza and in the Egyptian Museum. But Cairo was not a city of the ancient Egyptians. The city was founded by the Copts as Babylon — one theory holds that its name has nothing to do with the biblical city, but rather Bab il-On, the Gate of On. After the Arab conquest in 641, it became perhaps the greatest Islamic city in the world.

Its mosques and monuments are preserved as far back as the flood-recording Nilometer of 861 and the mosque of Ibn Tulun, built in 879. There are architectural treasures from almost every historical period since then, including a supreme run of Mamluk architecture, the dynasty which ruled between 1250 and 1517. It’s a cornucopia that compares with treasures from the Roman Baroque, or the Florentine Renaissance.

To plunge into Islamic Cairo ankle-deep — perhaps literally so, since the streets round here are not that well-kept — start with your back to Khan al-Khalili, and cross the road. You might recognise the two towering buildings, exuberantly striped and ornamented, from a famous painting by the Victorian artist David Roberts. These are the Ghouriya, a complex of religious buildings built by the last-but-one of the Mamluk sultans, al-Ghouri. They combine several purposes — a madrassa, or religious school with a mosque, is on the right. On the left, there is a mausoleum and a sabil-kuttab, or a combination of public fountain and elementary school.

The beautiful mosque of al-Ghouri is a good starting point. Its thick walls and complex entrance remove you from the raucous world of the street; an ingenious system of air circulation keeps the building cool and fresh. Inside, the light is rich and velvety; there are high windows of bright stained glass, greens against reds, and everywhere a transfixing mastery of ornament. The calligraphic verses from the Koran merge almost seamlessly into geometrical patterns and plant forms; the whole effect is restrained and organic.

Most of Cairo’s mosques are still in use and it’s important to approach them in a polite spirit, removing your shoes and asking permission to take photographs. In almost every case, the non-Muslim will be welcomed, though perhaps with a little bemusement, and sometimes with excessive deference. Most mosques, for some reason, are strewn with supine men, giving a very good impersonation of being asleep. The custodian of Barsbay’s mosque, after welcoming me in, officiously dashed about waking all of them up, telling them to sit up and make a good impression.

These beautiful buildings are effectively buried in the mud and chaos of Cairo’s urban life. Walking away from the Ghouriya, you find yourself in the middle of what seems to be the women’s underwear bazaar: stalls of vast bras and knickers in washload-destroying shades of red and pink and peach.

There are boys with vats of karkaday (hibiscus tea) on barrows, sacks of guavas, cotton bales, an ice-merchant carrying a glistening 6ft plank of ice on his shoulder; and suddenly you see the extraordinary vision of the Sabil of Tusun Pasha, with its Rococo styling and bulging walls, very like a miniature Paris Opera.

The Egyptian Government doesn’t seem to have its Islamic heritage high on its “to do” list. Some of the most fabulous stretches of Islamic Cairo, notably the street from al-Azhar to Bab al-Futuh, take place along streets that are like bomb sites.

Occasionally, a piece of exemplary restoration has taken place. There are two splendid medieval palaces that shouldn’t be missed: a merchant’s house, called Beit al-Sihami and, just by the Ibn Tulun mosque, the GayerAnderson museum, also known as the Beit al-Kritliya. Lucky old Major Gayer-Anderson had a well in his garden which turns out to be the underground entrance to the palace of the Sultan of the Bats, the evil genius of The Thousand and One Nights, where the Sultan’s seven daughters still lie asleep on golden beds. That’s what I call a water-feature.

In both houses, you can see the seductive rhythms of medieval domestic life; the rooms melt from interior to exterior, the purpose of each not firmly defined as the household would move around in search of coolness.

There are public and private spaces; the private areas, lived in by women, have mashrabiyyas, or wooden lattice-work screens, overlooking the public areas or the street — readers of Naguib Mahfouz’s Palace Walk will remember the erotic potential of these veiled openings, as the heroines peep out and even let their faces be seen by young men.

The mixed and fluid uses of buildings is very marked in Cairo. One of the loveliest of the sabil-kuttabs, Qaytbay’s, is no longer used as a neighbourhood fountain, but has gone on serving its function as a centre of learning — there is an excellent library on the upper floors in which you are made very welcome. Visiting one of the most ingenious and beautiful of all mosques, Qijmas al-Ishaqi, it is enchanting to overhear the noisy chanting of children from the attached kuttab.

The oddest mixture, however, is in the so-called City of the Dead, or the two great cemeteries. Though they were built as cemeteries, Egyptians always lived among the dead, and now they are thriving urban centres with frequent tombs interspersed. Here, in the Northern Cemetery, is an awe-inspiring sequence of late Mamluk mosques.

In a just world, the ornamental fantasy of the Qaytbay funerary complex, its dazzling lace-draped dome above all, would be as celebrated as the greatest of Venetian churches. In reality, you will have it all to yourself.

But you may be just as beguiled by the friendly, if slightly surprised, greetings from the inhabitants of this oddest of urban developments, as you walk along the streets afterwards.

Need to know

Philip Hensher travelled with Bales Worldwide (0870 7559851, www.balesworldwide.com), which offers five nights at the Nile Hilton hotel, Cairo, on a B&B basis, from £630pp, based on two sharing. The price includes flights with Egypt Air from Heathrow and transfers. Half-day sightseeing tour of Islamic Cairo with private guide costs £42pp (based on two sharing).

Reading: Islamic Monuments in Cairo, by Caroline Williams (American University in Cairo Press, £14.95). The Cairo Trilogy by Naguib Mahfouz (Everyman’s Library, £20).

Eating: Traditional and elegant: Abou El Sid, off 26th July Street, Zamalek(00 20 2 735 9640).

Chic and international: L’Aubergine, 5 El Sayed al-Bakry Street, Zamalek (738 0080).

Drinking: For chic, Nile-side settings try La Bodega, 157, 26th July Street, Zamalek (735 0543); Sangria, Casino El Shagara, Corniche El Nile, Maspero (579 6511), and La Sequoia, Aboul Feda Street, Zamalek (735 0014).

Go green: Half the £299 you pay for a ten-day Eco Egypt tour goes to a children’s home in Cairo. Departures on February 14 and September 5 with On the Go Egypt (020-7371 1113, www.egyptonthego.com).