The Budapest Museum of Applied Arts is one of the most extravagant and extraordinary buildings of its era. Its architect was Odön Lechner (1845-1914) whose work constituted an attempt to define a peculiarly Hungarian style, a Magyar parallel to what Gaudí was doing for Catalonia. Inspired by the V&A in London and embodying the hope that a nation could be encapsulated in the things it produces, it was set against a background of intense rivalry between the twin capitals of the Austro-Hungarian empire and Hungary’s deep desire to assert an intellectual and spiritual independence. Its exotic blend of eastern motifs refers to the Magyars’ origins in central Asia: the brilliant green and gold tiles of its roof were meant to evoke a dragon rising from the city streets, while the decorated planes of its walls echo the carpets and embroideries hung inside the yurts and tents of an earlier nomadic existence.

This search for an essence of Hungarianness makes the museum a perfect venue for the first major retrospective of a neglected corner of contemporary architecture.

The new Organic Architecture was forged by Imre Makovecz, a charismatic figure who made his reputation working for the state architecture department (the only job going, under communism). He made powerfully expressionistic and anthropomorphic concrete and timber buildings, a reaction against the system-built inhumanity of the state-sanctioned style. His political opposition finally saw him cast out, literally, into the wilderness, where he found an outlet for his architecture working in the forests of Visegrád. Here, in the early 1980s, he built a series of evocative structures in the woods, and the place became a base for subsequent generations of architects engaged by Makovecz.

Organic Architecture was defined by an effort to root building into culture and place, to find a local expression, first against a communist state that broadly attempted to homogenise and dumb down architectural culture across the bloc and then against a powerful wave of globalisation that was to prove almost as devastating to local culture and tradition.

The work that emerged represents a unique act of resistance and resilience to the conventions of contemporary design. Always at the fringes, these architects slowly built a language that embraced the organic, the vernacular, which alluded to myth and to darkness as much as to light. It was an architecture obsessed with meaning, which posited man not as a passive user but as a dweller who engages spiritually with the building.

Makovecz’s most spectacular buildings include the Farkasrét funerary chapel of 1975, a dark, sinister timber ribcage that alludes to the resurrection parable of Jonah and the Whale, and the exquisite church at Paks (1987), a sensual structure that emerges from the landscape to embrace and swallow the worshipper into its scaly body.

This is all set alongside the work of a generation of younger architects who emerged, first through their co-operation with Makovecz and later through the establishment of a journeyman school system that allows students to move between allied offices. Their work is usually small-scale – simple interventions into villages and small towns, a memorial, an extension to a village hall or school – but these architects are deeply embedded in place. Over the years, this work has solidified into impressive attempts to reinforce local identity, to give meaning to usually poor communities, to give their small settlements centres that were stripped out during the years of collectivisation. And it is done for almost unbelievably small amounts of money – these are buildings that grow out of the community, they are not imposed – radically different in nature to the “icons” of the west with which they are sometimes erroneously compared.

From the visionary high point of Makovecz’s most expressionistic work, the architecture of the organic school has mellowed a little, but the buildings remain unmistakable and have embraced every use from apartment houses to wineries. There is the rich, theatrical brick and timber of Dezsö Ekler, the sculptural invention of the Axis office, the post-modernism of Sándor Dévényi, the environmental responsiveness of the Kör Studio and many others.

Arranged around the museum’s brilliantly lit, Orientalist courtyard, the show is dominated by a spiralling white installation which, when reflected in a mirrored floor, forms a sphere spinning out from the dome above. It complements Makovecz’s inspirational drawings. It is rare to see beautiful architectural drawings in a contemporary architecture show (they have been supplanted by quick sketches) and his pencil compositions begin to build visionary worlds of light and dark, the mythical and the actual. Makovecz’s assertion has always been that there are two worlds, the world of what is and the world of what might have been, a yin/yang of light and shadow, reality, remembrance and hope. In his drawings of a tree and its roots, exposing a parallel world of darkness and complexity buried within the landscape, he challenges architecture to be about something deeper than mere appearance, more than the smooth, reflective ennui of glass and steel, and to engage with the earth, the land, memory and myth.

Until September 13