Charles Rennie Mackintosh: First retrospective reveals tantalising glimpses of what might have been

In 1909, two architects, born within a year of each other in the late 1860s on either side of the Atlantic, were engaged in the final stages of work that would define phases of their careers. The long life, large output and worldwide fame of the American, Frank Lloyd Wright, are well documented. For the architect working in Scotland and completing his most famous project, the Glasgow School of Art, the year would mark the end of the major commissions he would receive. When Charles Rennie Mackintosh died in London in 1928, he had built nothing of significance in his last 20 years. His entire estate was valued at £88.

Wright receives only a fleeting mention in the timeline of Mackintosh's life and work at the start of a new exhibition at the Royal Institute of British Architects (Riba). The two men never met, and the timeline merely points out that while Wright was completing the Robie House in Chicago, the "Prairie" project often called the "cornerstone of modernism", and was about to move on to other significant work, Mackintosh was pretty much done as a frontline architect.

For a Scottish architect whose reputation is based on local designs for handful of residential "dwellings" such as the Hill House in Helensburgh and Windyhill in Kilmacolm, and Glasgow's art school, and who is nevertheless regarded as "one of the leading figures of late 19th and early 20th century architecture", something extraordinary in his work must make him stand out.

In three small rooms at the Riba, the curator of Mackintosh Architecture, Professor Pamela Robertson, has tried to convey the magic and enigma of Mackintosh mainly through his detailed and exceptional draughtsmanship, first as a young apprentice, then later as the most creative partner in the dependable, well-connected, late-Victorian Glasgow practice of John Honeyman and Keppie.

The exhibition's focus on 60 original drawings, watercolours and perspectives is the result of new research which surveyed all the surviving documents from the firm during the Mackintosh years 1889 through to 1914 when "Toshie" and his wife, the artist Margaret Macdonald, decided to leave Glasgow for a period of "rest and recuperation" in Suffolk, but never went back home.

The research hoped to unearth Mackintosh's distinctive signature in previously missed major projects. That didn't happen. The survey of the practice's 250 works did, however, offer insight into the frustrations that still bedevil big practices: the exploitation of a subservient young draughtsman bringing new ideas to an established firm, but never getting due credit.

Drawings for the Glasgow Herald building in Mitchell Street (1894) – shown in the exhibition along with designs for the Daily Record building (1901) – hold Mackintosh's unmistakable imprint. Yet in the late 1890s his input into these and other projects was never publicly acknowledged. He told a colleague "Mitchell Street was designed by me" and added: "I hope when brighter days come I shall be able to work for myself entirely."

The same frustration was there in phase 1 of the art school. Mackintosh, aged 28, had been instrumental in delivering the design that won the art school commission. But, still a junior assistant, he received no invitation to the formal opening. The applause went to Honeyman and Keppie. He would need to wait till 1909 when the art school was officially completed to be acknowledged as its creator.

Much of the Riba exhibition centres on Mackintosh's "dwellings". He described his masterpiece, the Hill House, as "not an Italian villa, or an English mansion, or a Swiss chalet … it is a dwelling house".

The drawings, perspectives and models of the houses in Helensburgh and Kilmacolm show clients that must have trusted their chosen architect, and an architect who understood Scotland's 16th and 17th-century baronial vernacular, and yet could be bold and fresh when he pared it down.

Wright called his Prairie houses a "response" to the "Middle West landscape" that accentuated the beauty around them. In Mackintosh's hands, the same natural response looked quiet and dignified and humble. And though he never advanced enough as an architect to produce an equivalent of Wright's Falling Water, nor delivered anything that matched the drama of the Guggenheim Museum in New York, part of the Riba exhibition offers insight into a what-might-have-been Mackintosh.

In a row of small, beautifully constructed models of unbuilt work, all painted white and gently lit, there is an artist's town house (1899), and, from around the same time, a house and studio in the country, the Gate Lodge at Auchenbothie, and another house at Kilmacolm. The display is an imaginary Mackintosh Street, a "Toshietopia".

So why were they never built? It could be down to what James Macaulay in his book on Mackintosh simply calls his elusive "enigma". A better explanation is that after Mackintosh became a partner, clients who wanted orthodoxy went to Keppie, and those who wanted "the strange things" went to Mackintosh. And in turn-of-the century Glasgow, despite it being the empire's second city, wealthy clients comfortable at the edge of adventure were few, and Mackintosh himself lacked the salesmanship to secure new business.

Although Riba held a Mackintosh exhibition in 1953, the new show is billed as the first "substantial" overview "devoted to his architecture". And that academic choice – to limit the analysis only to exteriors – may ultimately be the reason why there may be difficulty here in accessing the soul and genius of the architect.

The inside and outside of Frank Lloyd Wright's greatest works are conjoined, the geometric symmetry of the interiors are anticipated by the exteriors. However, in Mackintosh's case, elevation drawings and perspectives have a limited impact on their own – essentially they reveal only a little of the magic found inside.

The clean, refined, almost feminine beauty of Mackintosh's interiors is integral to any understanding of his place in architecture. When it eventually arrived, his fame was bound up in the duality that exists between the outside and inside of his buildings. One without the other would create a sense that something important was missing. When the Glasgow School of Art was partly destroyed by fire last May, many wept. A lot of those tears were for the loss of what was inside that great building.

Mackintosh Architecture, Riba, London W1 (architecture.com) 18 February to 23 May