You know you are in Portugal when the pavement is trying to impersonate the ocean. And right now the ground beneath my feet is trying particularly hard. An elaborate mosaic of basalt and limestone, it sends waves of polished black and creamy off-white rippling across Lisbon's main square. They rush past the statue of Dom Pedro IV, ignoring him entirely – rather like the natives, who call the praca "Rossio" ("common land") in defiance of the ex-king whose name it officially bears. They roll past the fountains at either end. They even swirl beyond the limits of the vast plaza, south along Rua Augusta to the Praca do Comercio and the north bank of the Tagus, upwards and west to the Bairro Alto district, east into the tight corners of Alfama.

These intricate carpets of stone lend an antique feel to the Portuguese capital. Not least because they can be tough to walk upon – slippery when wet, lumpy and uneven when dry. I realise this when, climbing to the Chiado district, I lose my footing on an unsecured piece of the jigsaw, and nearly take a closer look at its composition.

But this is a rare concern. Paving aside, Lisbon does not do "difficult". It is a compact city, easily navigated and, happily for potential visitors, a mere two-hour flight from the UK (with which it shares a time zone). For all this, it is relatively undiscovered by British travellers in need of a city break.

There is a certain irony here. As the port where Vasco Da Gama began his attempt to identify a sea route to India in 1497, Lisbon is big on discovery. Like Rome and San Francisco, it lies scattered over seven hills. Its up-and-down terrain ensures lovely views at almost every turn, much as it once ensured that the city would develop in separate enclaves, each with its own distinct character. Most notable of these is Alfama, its name (and nigh-on claustrophobic net of crooked passageways) redolent of the era between the 8th and 12th centuries when the region's Moorish "occupiers" constructed their stronghold on this elevated bluff.

The Castelo de Sao Jorge, heavily remodelled in the 14th century once Lisbon had fallen to Crusader fire, still gazes across the rooftops, keeping an eye on the river and the Atlantic beyond.

Downtown basks in a different historic glow, having been rebuilt from scratch after the 1755 earthquake that levelled much of the city, while leaving Alfama undamaged on its solid crag. Airier than its neighbour, Baixa's clean, straight lines and narrow blocks exude sweeping 18th-century glamour.

Perhaps this explains the lack of multinational predictability in the area's shops (a theme that continues in Chiado). With a couple of exceptions, Rua Augusta and the surrounding lanes are dotted with locally-owned stores: clothing boutiques (some trendy, some decidedly dated), tabacarias, bakeries proffering colourful piles of cakes and pastries, and wine merchants where bottles of vintage port gather dust in the window.

The number of euros needed to liberate a few drops of the latter (well into three figures in some cases) could be enough to send you teetotal. But for the most part, Lisbon is an inexpensive city for British tourists. Public transport – such as tram 28, whose wooden carriages do clanking battle with the gradient, and almost clip the houses that lurk unnervingly close to the rails – is cheap and efficient. The myriad restaurants in and around the Bairro Alto offer plenty of options for good-value dining. Solar Do Duque offers the Portuguese staple of bacalhau (salted cod) for €8, while the (slightly) more upmarket Lisboa A Noite is a seafood dream, and does spicy octopus with baked potatoes for €16.

The Bairro Alto is the heart of the city's nightlife, its title ("High District") a classic case of stating the obvious. The lazy or romantic can reach it via the Elevador de Santa Justa, an iron lift, completed in 1902, which rises 45 vertical metres from Baixa to Rua do Carmo. Those who fancy a little exercise can ascend via a series of staircases that snake – at angles approaching 45 degrees – up the slope from Rossio.

The reward is an area alive with noise – but not until midnight, when the bars in the labyrinthine alleys west of the Rua da Misericordia click into gear. Mezcal is one such place. It serves potent caipirinhas for a bargain €3.50, but room inside is limited and, after paying for my drinks, I push back to the pavement – where things are just as busy. At one point I'm squished into the wall as the crowds jostle on a thoroughfare that, even when it was laid out, can barely have accommodated a horse and cart.

If this makes Lisbon sound like a medieval theme park, appearances can be deceiving. The prevailing mood is hip and young. MuDe, the Design and Fashion Museum, opened two months ago in a former bank on Rua Augusta that was midway through demolition when the irreplaceable nature of its marble counters was noted.

Stripped naked, MuDe (which means "change" in Portuguese) is an imposing exhibition space, its colourful contents seeming like items salvaged in a post-apocalyptic world – placed in display cases next to exposed brick and concrete.

East of the centre, meanwhile, the Parque das Nacoes has escaped white-elephant status. Once a dead industrial outpost, it was re-sculpted for the 1998 Expo, and has thrived since thanks to an aquarium, its riverfront restaurants and the Vasco Da Gama shopping centre. The trick is repeated west of Baixa in the Docas (Docks) area, where further eateries offer al-fresco cuisine below the 25 De Abril suspension bridge. And there is modernity on the streets, in the shape of the GoCars – yellow three-wheeled vehicles equipped with talking GPS guides. Tourists buzzing around Alfama while a polite voice points out the cathedral has become a commonplace sight.

The Tagus has a hypnotic effect on the city, pulling west towards the open Atlantic 10 miles away. Belem stands out as Lisbon's most alluring riverside district. The tussle between new and old continues here, the first camp represented by the Centro Cultural do Belem, where the modern artworks of the Berardo Collection include an Andy Warhol portrait of Judy Garland. The second is led by the Antiga Confeitaria de Belem, a Lisbon coffee-shop institution where golden pasteis – an inimitable type of sugary custard tart (the recipe is a closely-kept secret) – have been sold since 1837. Then there is the Mosteiro dos Jeronimos, a towering monastery founded in 1502 to commemorate Vasco Da Gama's grand voyage. The great man's tomb sits within.

The monastery hit the news in 2007 when Europe's leaders signed the controversial Lisbon Treaty in its cloistered courtyard. A plaque outside the entrance bears the signatures of all involved, including Gordon Brown, who famously arrived two hours after the ceremony. The PM was not the first Briton to be slow to appreciate the joys of the Portuguese capital. Canny travellers would do well not to follow his example.

Traveller's Guide

Getting there

The writer flew from Heathrow to Lisbon with TAP (0845 601 0932; One-way fares start at £48. EasyJet flies to Lisbon (0905 821 0905; from Gatwick, Luton, Liverpool and Bristol; and BA (0844 493 0787; from Heathrow.

Getting around

Lisbon public transport: Single journeys by tram or Metro cost from €€1.40 and €€1.30 respectively.

GoCar Tours (16 Rua dos Douradoures, 00 351 210 965 030; rents three-wheeled vehicles. The first hour costs €25, the second €20 and €18 per hour thereafter; full-day €89.

Staying there

Lisboa Tejo Hotel, 2 Rua dos Condes de Monsanto (00 351 218 866 182; Double rooms start at €87, including breakfast.

Eating & drinking there

Antiga Confeitaria de Belem, 84-92 Rua de Belem (00 351 213 637 423;

Doca de Santo, Doca de Santo Amaro (00 351 213 963 535;

Lisboa A Noite, 69 Rua as Gaveas (00 351 213 468 557;

Mezcal, 20 Travessa da Agua da Flor, Bairro Alto (00 351 21 343 1863).

Solar Do Duque, 69 Rua do Duque (00 351 213 426 901).

Visiting there

Berardo Collection, 2-5 Rua Rosa Araujo (00 351 213 192 300; Open daily 10am-7pm (until 10pm in July and August); admission free.

Castelo de Sao Jorge (00 351 218 800 620; Open daily 9am-9pm (until 6pm Nov-Mar); €5.

Mosteiro Jeronimos, Praca do Imperio (00 351 213 620 034; Open Tuesday-Sunday 10am-6pm (until 5pm October-April); €6.

MuDe, 24 Rua Augusta (00 351 218 886 117; Open Tuesday-Sunday 10am-8pm, until 10pm Friday and Saturday; free.

Ocenario de Lisboa, Doca dos Olivais (00 351 218 917 002; Open daily 10am-8pm (until 7pm in winter); €11.

More information

Lisbon Tourism: 00 351 210 312 700;