Barbara Hepworth always suffered from not being Henry Moore. Or, in fact, from not being any old Henry, John or Jacob. Sculpture being a man's business and all. Except, maybe it's not quite that simple. Certainly, Hepworth doesn't have the brand recognition that Moore does. But as a new retrospective at Tate Britain – her first for almost 50 years – makes clear, during the 1950s and 60s Hepworth was an artist of international standing in the way that Moore never really was. In 1950 she flew the flag at the Venice Biennale – and it's a Barbara Hepworth in Manhattan's UN Plaza, not a Henry Moore.

'Barbara Hepworth: Sculpture for a Modern World' is recognition that Hepworth's stock has been rising exponentially in recent years; that her abstracts now resonate more powerfully than Moore's looming figures and that her carvings in African hardwood have aged remarkably well. She certainly gets name-checked more than often than Moore these days, by designers if not artists. Hepworth is a true modernist icon in ways Moore is not.

It seems that Hepworth had planned that all along. One of the more fascinating elements of the show are her photographic collages, which first appeared in The Architectural Review in 1939, placing her works alongside modernist houses by the likes of Neutra. This now feels like a very smart move, positioning her work as part of the broader modernist project (and ensuring that she is now fetishised by the same people who fetishise Case Study Houses and Finn Juhl sofas). Indeed, the exhibition makes clear how much care and attention Hepworth  – the toughest of cookies – paid to show her work was well represented in art magazines and beyond.

Another joy of the show is a room dedicated to the marvelous Gerrit Rietveld Pavilion at the Kröller-Müller Museum in Otterlo, Holland, which has housed a permanent installation of Hepworth's work since 1965. For this exhibition, Tate Britain worked with architect Jamie Fobert and students of the RCA to create a temporary take on the Pavilion, housing six works from the late 1950s and early 60s.