Venetian children have taken to calling gondolas "Japanese boats" over the past few years. This is hardly surprising, because, apart from making trips with honeymoon couples, every one of these elaborately gilded craft spends its day ferrying intensely-scheduled groups of Japanese tourists up and down the Grand Canal. At the prices asked by the singing gondolieri, gondolas are, for the rest of us, a forbidden form of transport.

Luckily, old gondolas are employed as traghetti, or ferries, to take shoppers backwards and forwards across the Grand Canal at several points, and all for the bargain price of 200 lire - rather less than 10p. It is astonishing that this open secret is so little seized upon by day trippers and visitors on weekend breaks. For here is one of those near-perfect moments when, standing upright in a tipsy gondola insinuating its way between vaporetti, and string bag in hand, one can pretend to be one of the 70,000 or so surviving locals.

My favourite traghetto ride is across the Grand Canal to and from the fish and fruit and vegetable markets at Rialto. Not only are the market stalls a powerful sensual stimulus at six in the morning, when most tourists are snoozing in the city's costly hotels, but as the food in most Venetian restaurants is horrid - stale, overcooked and over-priced, as it has been since British tourists first arrived here in the 18th century - they are something of a lifesaver.

Most of Venice's best kept secrets are hidden well away from the Grand Canal, although after a trip to the markets, dip into Da Mori, a bar frequented almost exclusively by Venetians, and in particular by gondolieri limbering up for the day's lucrative "O solo mio"s with a stringent caffe corretto or two.

Even if you have a reasonable grip on Venetian dialect, everyone will know you are a foreigner at Da Mori: you will be the only person able to walk through the narrow door to the street without having to turn sideways. Unlike effete Brits, the working men of Venice are endowed with some of the broadest shoulders this side of the pages of Marvel comic books.

Suitably refreshed at Da Mori (try the local sweet, fizzy red wine, which is excellent on an autumn day), set off in search of secret Venice. On my biennial trips to the city, I rarely pass by the shabby-looking church of San Pantalon without stopping by to gawp at the extraordinary Baroque painting that fills its dark and lofty ceiling.

A 200 lire coin in the light-box brings Gian Antonio Fumiani's operatic trompe-l'oeil to all-singing, all-dancing life. Angels and saints appear to cavort up into the heavens, while others dangle their canvas legs over the side of the cornice above the veiled heads of black-clad ladies chanting decats of the rosary. This is much better than telly, but you will need to have a store of 200 lire coins in your coat pocket to keep this late- 17th-century version of cinerama glowing in front of your incredulous eyes. The bravura painting seems all the more poignant when you learn that, after toiling at it for 24 years, Fumiani fell to his death from the scaffolding.

There is nothing left of the painter's work today save what you see above you, which is quite enough for any British tourist brought up in a world of chaste churches knocked about a bit by Cromwell and strict, disciplinary chapels. There is, however, a butcher's block of saintly relics scattered throughout the rest of Venice; I cannot recommend too highly the tiny niche in a dark corner of SS Giovanni e Paolo, the city's cavernous 14th- century Dominican church, in which you find the foot of St Catherine, flesh peeling off tiny bones like old parchment.

Nor should you miss St Nicetus, an early Romanian bishop whose engagingly gruesome cadaver, cloaked in ecclesiastical splendour, rests away the centuries in the the venerable church of S Nicol dei Mendicoli (the church of Santa Claus, or Father Christmas, whose bones the Venetians claimed to have rescued more than a thousand years ago); the saint was "chiuso per il restauro" for some years, but is happily back in this pretty little church in the shadow of the city jail, where few tourists tread.

The most easily overlooked churches are those at the eastern end of the city, beyond the Arsenale, the old dockyards where the ships of the once invincible Venetian navy were built (a number 5 bus takes you through the Arsenale; otherwise it remains a military zone, and only a letter to the admiral in charge will allow you to visit here on foot). Here, by the municipal gasworks, is San Francesco della Vigna (started by Sansovino in 1534; completed by Palladio in 1572). Inside - you will normally be the only tourist - is one of my favourite paintings, the joyous Madonna and Child Enthroned by Antonia la Negroponte (1450), in which the Virgin poses in a rose bower flanked by orange trees. She is not as fine as Bellini's Madonnas (the artist's gorgeous, pouting mistress stood in for the BVM), but these are almost too easy to find (upstairs at the Accademia, first room on your left).

Another exceptional Madonna is the haunting Virgin who, given shape by some anonymous 13th-century mosaic artist, shimmers in gold and blue from the apse of Torcello Cathedral; this is the austere, yet magnetic deconsecrated church on the remote island of Torcello (number 12 bus from Fondamente Nuove) which also hosts an epic and truly disturbing 12th-century Apotheosis of Christ and Last Judgement on its west wall; you can almost feel the slathering jaws of hell sinking into your worthless flesh as you quake before this medieval nightmare.

On the subject of islands on the fringe of Venice, there are three others I would recommend, but the last comes with a proviso. The first is San Francesco del Deserto (gondola from Burano, reached by a number 12 from Fondamente Nuove) to visit the lovely garden tended here by the Franciscan monks. The second is San Lazzaro degli Armeni (number 10 from Riva degli Schiavoni), where Armenian monks will, if you ask nicely, show you their revelatory collection of books and manuscripts. Some date back to the fifth century and are a privilege to be able to read in the sanctity of the venerable library here.

My third island is a difficult one. Not only must you negotiate a trip over to Lazzaretto Vecchio by punt (not easy), but you must also endeavour not to return with a stray dog in tow - so long as the British quarantine laws continue. For here, among classical architectural fragments, Venice hides its canine waifs and strays, and a pathetic spectacle it makes.

Having met the monks and their garden on San Francesco del Deserto, it is worth remembering that Venice is home to a bed of exquisite gardens, nearly all of them hidden behind towering walls flanking the city's shoulder- wide alleyways. Or, in the case of the romantic vegetable garden cultivated behind Palladio's Il Redentore (that most perfect church, consecrated in 1592 and built to celebrate the end of the plague of 1575-76 that killed 46,000 Venetians) behind a monument visited by countless tourists, precious few of whom know what greenery sprouts in the shadow of its Byzantine dome.

By now you will be tired and hungry; after all, we have covered a fair amount of ground, or water, in search of secret Venice. May I recommend lunch at the Rosticceria San Bartolomeo (Calle della Bissa, off Campo San Bartolomeo)? You will have to stand up and eat, I'm afraid, but you will be very much in the company of Venetians; join them as they tuck into heaped and cheap plates of fish stew, liver and polenta.

This pit-stop will give you the strength to tackle one of two final and fascinating trips to see the Venetian lagoon's all-but-secret wildlife (there is more to Venice that pigeons and cocky little dogs drawn from paintings by Carpaccio); take your pick of a rainy afternoon spent in the gloriously old-fashioned and museologically incorrect Natural History Museum (Fondaco dei Turchi), or take a trip out to Chioggia, a working- class Venice in miniature, as everyone here describes it. Chioggia is at the furthest reach of the lagoon. Home to one of the finest fish markets in Europe, it is also the stamping ground of Signor Bossi's extreme right- wing northern Italian separatist movement. Admire the fish, but do not talk politics; for here you can even afford to ride around the canals on a "Japanese boat", and that must be the greatest Venetian secret of all.

City essentials: Venice

Jonathan Glancey flew from Gatwick to Venice with Alitalia, not an experience he would repeat, however, since the DC-9 developed an engine fault immediately after take-off and he spent an unscheduled two hours on the ground at Brussels airport. Next time, he says, he will try a different airline. Italy Sky Shuttle (0181-748 1333) has November flights for pounds 163 on a Monarch charter from Gatwick, or pounds 192 on British Airways from Heathrow.

From the airport to Venice, a taxi will cost around pounds 25. Local buses run every 30 minutes or so for pounds 1.

Ask the Italian State Tourist Office, 1 Princes St, London W1R 8AY (0171- 408 1254) for a map of the city, but do not expect it to be entirely accurate.