“Wellness” is all the rage at the fancier end of modern office development. Anxious to entice valuable employees away from the comforts of working from home, or from defecting to rivals, companies offer them spas, gyms and views of greenery. Proposals for gigantic office blocks in the City of London now come garnished with shrubs and trees and other forms of urban parsley dozens of storeys up in the air. There’s a related mania for running green stuff up the outside of all kinds of buildings. All too often these plans exist more in the realm of gesture than reality, and come without full consideration as to what it actually takes for plants to flourish some distance from the ground.

The idea of achieving wellbeing through multistorey vegetation is not new. It was put into practice a half-century ago with a building known officially as Gateway House, then Mountbatten House and now Plant, more popularly known as the “Hanging Gardens of Basingstoke”. Designed by Arup Associates and the plantsman James Russell (1920-96), it provides six levels of gardens stepping up a sloping site, arranged so that its interiors would never be far from views of greenery, transporting office workers from the mess of roads and office blocks in which it stands up to a world of lush terraces that seem to flow into the surrounding hills. Created during a time when Basingstoke was a “London overspill” area – a government designation that brought with it a smidgin of the forward-looking ideals of new towns, of providing new lives for escapers from the crowded metropolis – Gateway House was to be a model enlightened workplace for the then-200-year-old paper-making company that commissioned it, Wiggins Teape.

Now, having fallen into some neglect, the building and gardens, which were Grade II-listed in 2015, have been brought back to life by an array of landscape architects and architects – Grant Associates, Studio Knight Stokoe, Twelve Architects and Feilden Clegg Bradley Studios – whose combined approach has been respectful and discreet, rejuvenating the building and gardens, while adapting it to such things as changing climate and the need to tolerate drought. Their clients are the investors Mactaggart Family & Partners and Longstock Capital, who felt that the attractions of the building would overcome a less than buoyant market for office space. It is now a building to be let to multiple tenants; the AA has taken a chunk.

Arup Associates were the architectural wing of the company founded by the great British engineer Ove Arup (1895-1988), who specialised in turning the dreams of modern architecture, from Lubetkin’s penguin pool at London zoo to the Sydney Opera House, into reality. When acting as architects themselves, the practice that bore his name was relatively restrained and considered, while faithfully following modernist principles. For Arup Associates, the look of the building had to be closely connected to the way it was built. There had to be integrity and consistency of thought running through the whole project.

With Gateway House they designed a grid of concrete pillars and shallow, pyramidal ceilings that give a sense of substance and unity throughout. The exterior is in steel, bronzed aluminium and glass, somewhat in the style of Mies van der Rohe, except that the blocks step up and down with an informality that the German-American master would never have countenanced. As the building was designed at the time of the 1973 oil crisis, there are overhangs to shade the interiors from the sun, and other measures to reduce the need for air-conditioning. It is a building with strong horizontals, a stack of planes that emphasise the flow of space from inside to out.

You ascend on arrival to a spacious entrance portico that leads to a generous reception area in the centre of the building from where, thanks to the slope in the land, you can go down as well as up to the office floors. Mostly, the architecture is dignified and calm, acting as a foil for the planting. James Russell, who had until then developed a quiet celebrity designing gardens in the grounds of country houses, here created a range of moods with an eclectic array of native and imported species, some of them gathered on his plant-seeking trips abroad. At Gateway House there are gardens themed around colours, such as gold and silver, and scents and seasons. Russell designed a wisteria terrace and a vine terrace, areas inspired by Japan and another dedicated to herbs, and an irregular pond stocked with coloured carp. Climbing roses scaled the corporate elevations. Trees were planted at the edge of the site, into whose now mature canopies office workers will (when they are not looking at the terraces or the countryside beyond) be able to gaze.

The whole is a three-dimensional ramble through spaces intimate and expansive, sometimes connecting with the landscape beyond, sometimes looking inward to courtyards. It is a cubistic hillside, a stately home and – its landscape rearranged for a less hierarchic age – as enchanting a headquarters for a stationery company as you could ever hope to see. It is, for all its variety, unified. It is miraculously verdant, thanks to the attention paid to the hidden technicalities of soil depth and irrigation, of exposure and shade. The interior is suffused with green-tinged reflections.

Much of the work of the £32m renovation is about preserving and enhancing these qualities, with such unnoticed but essential actions as polishing travertine paving, replacing soil that had become compacted, and refurbishing the curtain walls, while making a few adjustments and updates. A new helical stair swoops down from the reception area to the lower levels, and new spaces have been formed for communal dining. All of which is not only for the private delight of the companies renting office space: part of the gardens are accessible to the public, from where most of the rest is visible. Outsiders are welcome to wander into the reception area and go to the cafe there.

Gateway House started something. Peter Foggo, the architect at Arup in charge of the project, went on to work on Broadgate, the 80s office development in the City of London created by the developer Stuart Lipton that set new standards in architectural quality and the design of open space. Current aspirations for wellness owe much to Broadgate, which in turn owes much to Gateway House. Many architects dream of getting plants and gardens to climb up their buildings, but anyone who really wants to know how to do it should make a trip to Basingstoke and see its slice of 1970s Babylon.