‘Valleys breathe, heaven and earth move together,/ daisies push inches of yellow air, vegetables tremble,/ grass shimmers green…’ The characteristic undulations of the voice of the Beat poet Allen Ginsberg greet the visitor on entering Wales Visitation: Poetry, Romanticism and Myth in Art at the National Museum Cardiff. Bearded and mellifluous, projected to mythic proportions across a vast expanse of wall, Ginsberg is seen reading his poem ‘Wales Visitation’ on American television in 1968, telling less of visits than of visions.

What was the Blakeian, Buddhist, drug-sampling poet doing in Wales? LSD. What he’s doing dominating an exhibition so thoroughly Welsh, formed almost entirely from the Museum’s impressive national collection, is less immediately explicable. The poem makes no attempt to deny his role as a benign intruder in an unknown land, even as it conjures a visionary connection with the landscape. Nevertheless, Ginsberg acts as bardic spokesman for the exhibition (detachable headphones allow you to navigate the show with words like ‘bloomlets’ and ‘tree-nooked’ chirping in your ears), there to direct our experience of landscape as something both entirely natural and unfathomably foreign.

This quality is the ‘exultant strangeness’ identified by Graham Sutherland on a visit to Pembrokeshire in 1934. The museum holds Britain’s largest collection of Sutherland’s work, as well as having recently acquired a superb collection of Welsh landscapes by John Piper. These are two artists integral to 20th-century British Neo-Romanticism. In the exhibition’s soaring central atrium, contemporary works by Clare Woods and Keith Arnatt assume Neo-Romanticism’s twisted, agitated reinterpretations of the pastoral, while Richard Long’s stone circle of jagged Welsh slate appears to have been beamed down, UFO-like, by the light-filled dome directly above. This stark centrepiece competes with the acid greens and hot pinks of large late works by Sutherland, colours crystallised in the artist’s smaller, mixed-media studies of natural found objects. The jewel-like works are hung in the manner of an altarpiece or shrine around a glass case revealing the objects themselves — knuckles of twisted wood and mottled stone, studio relics flecked with viridian and ochre. The defining atmosphere is pointedly spiritual, yet grounded in material objects — as though one has stumbled upon the abandoned apparatus of some elaborate pagan ritual.

Upstairs, a section on folk art presents a Mari Lwyd costume (a gleeful pantomime horse decked in tinsel trimmings, a glimpse of yellowing equine teeth unmasking the skull beneath), along with various other curiosities including a rag-ribboned ‘wren house’ and a wonderfully knobbled wassail bowl, writhing with human and animal forms. British folk art is ready for reassessment, with the first major survey on the subject to be held at Tate Britain in June. Nevertheless, such works can appear clumping and cold when taken out of context, amputated from the rituals that enlivened them. As a result, there is a strange melancholy to this section of the exhibition. In the short film A Setting, by Cardiff-based artist Anthony Shapland, an old man at a window regards the rise of a Romantic moon in the gradual gloaming, its light eventually superseded by a bare bulb reflected in the windowpane. Perhaps any modern approximation of Romanticism is fated to be similarly stumped by self-consciousness.

Nevertheless, it seems our minds are ripe for re-enactments of the Romantic imagination. In its eclectic range and elaborate narrative, the exhibition is comparable to Tate St Ives’ 2010 exhibition The Dark Monarch: Magic and Modernity in British Art, and similar preoccupations are present in Tate Britain’s current exhibition Ruin Lust. However, it’s easy to forget that the Neo-Romantics were once regarded as little more than kitsch — it was only after the Barbican’s seminal 1987 exhibition A Paradise Lost: The Neo-Romantic Imagination in Britain 1935–55 that artists such as John Minton, David Jones and even Graham Sutherland were grudgingly incorporated into the story of 20th-century British art. Even then, their work was regarded with some suspicion well into the 1990s.

What draws us back to these works? Is it a longing for figurative visions in an age of digital immateriality? For aesthetic enrichment at a time of austerity? Or perhaps it is part of an wider engagement in the landscape, emerging from ecological threat? This is not an exhibition that boasts grand theories, backed up by far-flung loans. It simply reveals a rich seam in our human thinking, and celebrates the land that has long inspired the excavation of such thoughts. Well worth a visit. Or rather, a visitation.