If Venice ever sank into its lagoon, the world-wide tourist industry might never recover. Hundreds of thousands of visitors fill every crevice of this floating architectural wonder every year with their bum-bags and dodgy outfits.

But you don’t have to become part of the tourist circus if you choose to visit. All you need is a proper guidebook, lots of patience and a pair of blinkers to achieve your sought-after romantic break.

Having reached Venice by means of a leisurely two-day train journey from London via Paris and Zurich – a highly-recommended buffer between the real world and your holiday time – my partner and I had plenty of time to absorb our Time Out guide to the northern Italian city.

Determined to avoid extortionately-priced water taxis, we jumped on the Vaporetto (water bus) outside the train station and headed down the Grand Canal.

Joining the crowds at the city’s main harbour, we bounced our wheelie suitcases over the trachyte and sandstone pavements, passing naff restaurants, lanky teenagers and tacky carnival masks as we passed through the world’s most famous piazza – St Mark’s Square.

The crowds who “infest the Piazza... pursue you along the Riva... hang about the bridges” – as first described by Henry James in 1881 – haven’t thinned out.

This formerly isolated playground for rich merchants, aristocrats and artists, who loved nothing better than a masked ball or five, has become ‘Venice Land’, complete with the gondola rides.

Once inside the Ca’ dei Conti hotel, a lush converted 17th-century aristocratic town house, we sank on to our bed’s embroidered covers, comforted by this luxury after the shock of the city.

That night we planned to get away from all the uninvited guests intent on spoiling our holiday, and walk as far away from St Mark’s Square as you can on an island that’s three miles long and two miles wide.

We were looking for the city that inspired the painters Carpaccio and Bellini, not the sliced meat and cocktail version fed to tourists.

Walking out along the harbour, past huge luxury yachts towards the tranquil, woody area of Sant’ Elena, we found a local restaurant, Al Diporto.

Sitting with many Italian families in one of the open streets of the Castello district, we feasted on freshly-caught sea bass, prosecco and polenta (cooked cornmeal, a Venetian speciality).

Wandering back along the shoreline, watching the lights flickering on the adjacent island of Giudecca, we slipped past the crowds – who seemingly wished to stand in St Mark’s Square for their entire stay – and got back to our hotel, smug with holiday victory.

Having proved it was possible to get away, we spent the rest of our days trying to lose everyone else, or to simply get lost. And surprisingly, we discovered that most of Venice is free from tourists.

An easy way to make an instant escape is to catch a boat to one of the neighbouring islands. La Giudecca, to the south of Venice, is a gondola-shaped strand of eight islands. With a wonderful view of the Venetian skyline, it is the perfect place to watch the sun go down. On advice from ‘those in the know’, we headed for the Cipriani restaurant, in search of a taste of Venice’s legendary luxury and glamour.

Cipriani encapsulates that history – and can even lay claim to inventing the Bellini cocktail back in 1931, when Giuseppe Cipriani set up Harry’s Bar on the mainland.

We were seated – naturally – a table away from Yoko Ono, Sean Lennon and his 23-year-old model girlfriend Kemp Muhl.

Drinking prosecco and swallowing wafer-thin pieces of carpaccio (sliced raw beef – another Cipriani invention), we weren’t entirely sure which view was the more fabulous: the sight of the dome of St Mark’s, or Yoko’s profile.

And after a personal greeting by Giuseppe’s son, 77-year-old Arrigo Cipriani, we felt as though we had tasted a little slice of history.

Buoyed by that glamorous meal, I decided next day that taking a gondola ride in Venice was important. Booking online with Viator (viator.com) we went for broke with the all-singing, all-accordion-playing version.

Hilarious, genuinely romantic and definitely good for your ego, we watched other tourists look jealously on as our singer rolled out all the hits, and grinned like idiots.

Last day – last lovely meal at the traditional Osteria da Alberto.

After a brief look at the menu, we settled on a Venetian classic: red wine and heavenly plates of oily strings of spaghetti flavoured with clams, chillies and garlic. I think I’m in love.

Factfile

Natasha Rush travelled to Venice with Railbookers, which offers European short breaks and holidays by train for independent travellers, not groups. She stayed one night at the Schweizerhof Hotel in Zurich and three nights at the Ca’ dei Conti Hotel in Venice, both B&B, on a ‘Venice via the Alps’ package from £589 per person. Package includes travel by Eurostar and onward to Venice, and return journey by air. All Railbookers packages return to London by BA, but connecting flights can be arranged to Manchester and Edinburgh. Railbookers reservations: 0203 3270800 and railbookers.com.