First thing in the morning, I stepped outside my bedroom on to a vertiginous balcony that is embedded in architectural history, before descending four storeys to the canteen. Indulging in a sunny breakfast sitting outside was a treat in itself, but in this case my enjoyment was doubled by having just slept inside the world's first Modernist building: experimental, utopian yet ultimately doomed by the vagaries of German history.

I was in Dessau, mid-Bauhaus pilgrimage between the nascent days of this seminal art and design movement in Weimar and the end of the German trail in Berlin. A new Barbican exhibition, Bauhaus: Art as Life begins tomorrow, the largest of its kind in the UK for more than 40 years, with exhibits loaned from Weimar, Dessau and Berlin. Apart from the aesthetic revelations of my journey, what became clear was that despite its short life (1919-1933), Bauhaus influence has been all pervasive, bringing us white walls well before Minimalism, flatpack furniture before Ikea, utilitarian style shops before Muji – and leaky flat roofs. Not to speak of chairs without legs.

For a visitor covering the ground as I was, the trail reflects modern German history itself, from the First World War to the economic hardship of the Weimar Republic, the rise of the Nazis, Allied bombing during the Second World War, the political division of West and East and, finally, German unification. Geographically it propels you intriguingly from the depressed former East into the pumping heart of the new Berlin. No other creative movement has been so inextricably mixed with history, nor spanned such a divide.

I covered the 570km revolutionary trail by predictably efficient Deutsche Bahn (German railway), shooting across the plains of eastern Germany past industrial tangles of pipes and chimneys, graffiti-splattered derelict buildings, wind-farms and towns edged with neat vegetable allotments beside bland housing estates. Further south, vistas of pine-forested hills and meandering rivers looked distinctly more mellow. Life on board local trains and ICE (inter-city express) was never dull, between clipboard-wielding apparatchiks and TGV-style buffet cars with baby-pink handrails and the dish of the day, sausages and potato salad (with Becks, naturally). There was no danger of missing a connection, either, as despite my schoolgirl German, an English-speaking passenger would always obligingly pop up.

Weimar was a cultural shock. I had no idea how rich an intellectual past it had, well before Walter Gropius, the Bauhaus mastermind, stepped onto the scene in 1919. Every street commemorates a local luminary, from Goethe to Schiller, Nietzsche, Bach and, much later, Marlene Dietrich, so it's not surprising that its chocolate-box charm has been recognised by Unesco as World Heritage grade.

Even my hotel, the Alt-Weimar, housed the great educationalist Rudolf Steiner for a time at the end of the 19th century. The building was converted in 1909, with wood-panelled dining-rooms much appreciated by beer-swilling, party-loving Bauhaus students. My own experience consisted of a surprise gourmet menu, with Riesling and ending with a beautiful Constructivist-style dessert. Upstairs, the room was spartan yet functional, a foretaste of the Dessau Bauhaus experience.

Thomas, one of the architectural students employed for the "Bauhaus Walking Tour", showed me the sights. At the Bauhaus University, I was impressed by a staircase mural by Oskar Schlemmer, although it turned out to be a reconstruction, the original destroyed by a Nazi director of the school, post-1926. Then, as we stood in Walter Gropius' reconstructed office to admire his furniture designs and Wagenfeld lamp, Thomas threw out insights into Bauhaus theory and ideological conflicts. Gropius's aim to tighten the links between art, crafts and industry attracted dynamic input from greats such as Paul Klee, Wassily Kandinsky, Josef Albers, Herbert Bayer, Johannes Itten and Laszlo Moholy-Nagy.

A stroll through the park flanking the Ilm river led us past Goethe's summer house to the prototypical Modernist house, the Haus am Horn, built by students for the 1923 Bauhaus Exhibition. For an architectural lightweight like me, this proved less inspiring, despite its historical significance. However, back in the centre, the modest Bauhaus Museum brought illuminating surprises, from a cradle to carpets, textiles, tableware and graphic arts. In 2015, a new museum will bring together hundreds more Bauhaus designs now in storage.

Dessau, a couple of hours north-east, was a complete contrast: quintessentially bleak, industrial East Germany. After losing three-fifths of its buildings to Allied bombing it is now depopulating in the wake of reunification. However, it boasts the world's first Modernist building (comprising school, workshops and student accommodation) and six semi-detached "Master Houses" brilliantly designed according to function, light and privacy. Gropius' own is now under reconstruction.

On top of that, a 20-minute tram ride away is the Törten Estate, an experimental garden city with three versions of terraced social housing. Here, building time was reduced to just six hours per house, fusing efficiency, economics and functional design, as well as green elements such as composting and vegetable gardens. Perhaps most moving of all were the fragments of owners' tastes: many had replaced windows and doors, added wallpaper, patterned lino and fanciful furniture.

Following renovation of the glass-walled Bauhaus building, visitors can now sleep in the lofty students' rooms, eat in the canteen and drink in the buzzy "Klub". In this second incarnation of the school – moved from Weimar in 1925 due to budget cuts by the Nazis – the focus shifted from arts and crafts to architecture with an industrial aesthetic, in tune with Dessau's hi-tech nature. In 1930, the exhausted Gropius was replaced by the legendary Mies Van der Rohe.

Two years later political pressures forced the Bauhaus to move again, this time to Berlin. By then the power of the National Socialists proved insurmountable, forcing total closure in 1933, and the Bauhaus diaspora.

It takes 90 minutes by train to travel from Dessau to Berlin's impressive new Hauptbahnhof. From there I made my way to the Bauhaus Archives and Design Museum, yet another ground-breaking design by Gropius – though built in 1979, after his death. Inside, exhibits included Marcel Breuer's modern classic, the first chair to feature a bent-steel frame. Suddenly the design history was all clicking into place. This sense was reinforced later when I walked past the Hotel Berlin, a sprawling Cold War building that seemed to encompass Bauhaus aesthetics. The movement never stopped: there is now even a Bauhaus app for your phone. And "my" balcony is part of design history.

Travel essentials

Getting there

You can fly to Frankfurt with Lufthansa (0870 8377 747; lufthansa.com) or BA (0844 493 0787; ba.com) from a rangeof UK airports. Deutsche Bahn (bahn.de) offers fast and frequent rail connections to Weimar, Dessau and Berlin. Flights from Berlin's Schönefeld airport to the UK areoperated by easyJet (0843 104 5000; easyJet.com) and Ryanair (0871 246 0000; ryanair.com); flights from Berlin's Tegel airport are by BA and Lufthansa.

Staying there

Alt-Weimar Restaurant and Hotel, Weimar (00 49 3643 86190; alt-weimar.de). Doubles from €85, including breakfast.

The Elephant Hotel in Weimar (00 49 3643 8020; hotelelephantweimar.com). Doubles from €111, room only.

Bauhaus Dessau (00 49 340 6508 318; bauhaus-dessau.de). Doubles from €35, room only.

Visiting there

For information on Weimar's Bauhaus walking tours, see weimar.de. Two-hour group tours cost from €85 per group.

Day tickets to Bauhaus sights in Dessau (00 49 340 6508 25; bauhaus-dessau.de) cost €15.

The Bauhaus Archive/Museum of Design (00 49 302 5400 20; bauhaus.de) in Berlin costs €6 (closed Tuesdays).

More information

The new Barbican exhibition "Bauhaus: Art as Life" starts tomorrow, until 12 August. Tickets £10 (barbican.org.uk)

Bauhaus Travel Book (Dumkont, 2012).