Many objects we take for granted and much of our visual environment are the result of work by students and staff of the RCA: you see its influence in the work of Henry Moore, Barbara Hepworth, David Hockney, Peter Blake and Tracey Emin — whose piece, The Perfect Place to Grow, gives the anniversary exhibition its title.
This remarkable college's DNA can also be found in the gardens of Edwin Lutyens and Gertrude Jekyll, the shape of a Land Rover or an Aston Martin DB7, the chairs of Robin Day, even an NHS bed and the 125 InterCity train.
RCA Rector Dr Paul Thompson has co-curated the exhibition with Robert Upstone of the Fine Art Society, formerly head of British modern and contemporary art at the Tate.
As a former director of the Cooper Hewitt Design Museum in New York, Thompson is no stranger to curating interesting shows, but this one has been a challenge. "We didn't want to fall into the trap of doing design decade by decade as a kind of roll of honour," he says.
"There was just too much work by former students and staff. Instead, the show has four themes: art for industry, public purpose, personal expression and political expression."
The RCA was founded in 1837 as the Government School of Design to improve the quality of design in the ceramics, textiles and ornamental crafts industries. One student, Christopher Dresser, enrolled in the school in 1847 aged just 13. Later he became the world's first "industrial designer".
James Dyson, today's most innovative design entrepreneur, joined the college in 1966 at the age of 19. The designs of both have impacted on the way we live: some of Dresser's metalware is still in production by Alessi, while Dyson's vacuum cleaners have conquered the world.
Renamed the Royal College of Art in 1896, it became an independent institution, awarding its own degrees, in 1967. It was not an easy decision for the college to include fine art, as opposed to the "useful" applied arts, among its courses but it can now claim to have helped train some of the art world's biggest hitters.
However, the RCA's world reputation rests in the seminal designers it has produced: Robin and Lucienne Day met at a college dance in 1940 and their work continues to influence design.
Robin's Hille Polypropylene Chair is the world's best-selling chair — available in 62 countries. The show includes Day's chair, plus a rarely seen cocktail cabinet from 1951, alongside fabrics by Lucienne.
The Fifties and Sixties saw the rise of designers such as David Mellor, who was behind a vast range of products from traffic lights to his now-signature cutlery. The show includes his Embassy cutlery range, alongside work by more recent graduates, such as Konstantin Grcic furniture designer Tord Bontje; Ed Barber and Jay Osgerby, designers of the Olympic torch, and Thomas Heatherwick, designer of the 2012 Olympic cauldron and also of the latest London bus.
The college has also had a key role in British fashion, with designers such as Ossie Clark, Bill Gibb, Zandra Rhodes and Philip Treacy. On the political front, the exhibition includes work by suffragette Sylvia Pankhurst, who was imprisoned in Holloway while a student at the RCA. She designed a brooch based on the prison's portcullis gate.
The Perfect Place to Grow: 175 Years of the Royal College of Art; RCA, Kensington Gore, SW7 (rca.ac.uk) from November 16 to January 3, 2013.