We are all trapped in the cultural canon. The allure of the famous artist or designer can be both irresistible and lucrative: if you want to create a blockbuster exhibition or need people to attend your festival, then an established creative star is your man. And he likely will be a man, and more than likely a white one.

Therein lies the problem with the canon – we require those within it to keep the coffers of our galleries and our festivals full, yet while those on the inside grow ever-more famous, others get sidelined or written out of history. The creative industries wring their hands about this, and about the lack of diversity among those entering their worlds, and yet still the problem endures.

It can be difficult to challenge these established systems. In January this year, as part of an event staged by the artist Sonia Boyce, John William Waterhouse’s painting Hylas and the Nymphs was removed from the walls of the Manchester Art Gallery, and a storm of Twitter commentary and newspaper think pieces was set loose. Boyce and the gallery were met with vitriolic cries of censorship and the curators were compared with Nazis.

But beyond the raging about feminism gone mad – the removal was viewed largely as being due to the painting’s depiction of seven young topless female nymphs – Boyce was making a deeper point about the decisions of which artworks are shown in our museums, and whether we should blithely accept that famous artworks such as Waterhouse’s should always be featured. Her intervention at MAG connects to her ongoing examinations about which artists feature in the story of British art, and who is left out.

Speech Acts, a new exhibition at MAG, curated by Hammad Nasar with Kate Jesson, continues these examinations, though – perhaps wisely – without the big gestures of the Waterhouse action. The show is rooted in the Black Artists & Modernism (BAM) research project, a three-year academic investigation instigated by Boyce to examine how artists of African and Asian descent in Britain feature in the story of 20th century art. As part of BAM, the team has conducted an audit into the amount of artworks by black and Asian artworks that are held in collections across the UK.

Through a wide-ranging exhibition, Speech Acts hopes to prompt questions of who gains entrance into the canon of art, and who gets archived. But it also delves deeper into museum practice, examining why galleries struggle to combine work of different mediums – design alongside art, for example – and what limitations the ‘artist biography’ and even the authoritative wall texts that accompany art exhibitions place on our understanding of artworks. There is also a questioning of artistic networks, and of which ones are given recognition over time.

At the centre of Speech Acts is the recreation of a gallery space from the 1970s which brings together many of these ideas. The LYC Museum & Art Gallery was founded and run by Li Yuan-chia, a Chinese artist who moved to London in the 60s and exhibited at the Lisson Gallery in the city. He then moved to Cumbria and set up LYC, which operated between 1972-83, and was an unusual, pioneering and prolific space, exhibiting the work of over 300 artists, and hosting four exhibitions a month, an incredible rate of production.

Li’s commitment to the project was total – he built the museum himself, undertaking all building, plumbing and electrical work, and also designed and printed catalogues for each show. He also created a space for children to play in at the gallery, which MAG has also done as part of Speech Acts.

LYC showed a mix of local artists alongside famous figures such as Paul Nash and Barbara Hepworth, and the gallery also championed pioneering installation and video artists including Shelagh Wakely and Stansfield/Hooykaas as well as contemporary artists such as Lygia Clark and Andy Goldsworthy, who went on to gain international renown.

With this level of productivity and influence, you would think that Li Yuan-chia and the LYC would be easily recognised names to those interested in British art, and yet they are not. Li is recognised to some extent for the art he created individually but the gallery is largely forgotten. This might seem incongruous, yet of course it happens all the time: some movements enter the canon, others drift out of sight.

In a text accompanying Speech Acts, Sonia Boyce quotes the artist and writer Rasheed Araeen who apparently alleged that when a black-British artist’s work is purchased by a public collection, it then goes into cold storage. “This harsh comment suggests a fundamental contradiction,” writes Boyce, “that the purchased work is of sufficient merit to be acquired and held in trust for the nation; yet, that same artwork, once in the collection, will be left to languish – if not forgotten, then certainly to remain unseen.”

The most common scenario where work by black and Asian artists might come out for display is when an exhibition specifically examining work by these groups is curated. A similar exercise occurs when museums examine works by female artists of a particular period or genre of work. The work is revealed and yet is still kept outside of a wider conversation with artworks of a similar period or movement.

Speech Act avoids this predicament simply by grouping artworks not by who has created them but by visual or conceptual links. It leads to some interesting juxtapositions: works by the artist and designer Eduardo Paolozzi, the artist Anwar Jalal Shemza and the textile designer Barbara Brown are displayed alongside each other, linked by repeated patterns across their work.

Other repetitions can also be seen across the abstract works of Bridget Riley, Fahrelnissa Zeid and Kim Lim. In the room displaying the LYC gallery reconstruction, the curators also place works by Francis Bacon and Lucien Freud, part of another ‘school’ of the time, but one which has gone on to gain huge international recognition. A space devoted to works exploring self-identity brings together works by Rasheed Araeen, Lubaina Himid, Li Yuan-chia and David Hockney, among others.

It is interesting to apply some of the ideas contained in Speech Acts to other creative fields, especially those that operate outside of the museum system. The ‘commercial arts’ of design and advertising may occasionally pop up in gallery spaces though the canon for these fields is usually defined by books or via teaching in art schools.

The scope for individuals and groups to be left out of design and ad history is therefore easy to imagine. When the London Transport Museum exhibited its recent ‘Poster Girls’ exhibition, celebrating the work of female illustrators for the London Underground, it was striking and depressing to hear of how artists who may have been of equal stature to their male contemporaries when they were working, had fallen entirely out of the design canon.

Looking at the contemporary picture of how reputations in these fields are established is illuminating too. Fame comes usually via appearances at conferences or on awards jury panels, with industry figures often making repeated appearances at both, solidifying their place within the contemporary canon. These groups will often be overwhelming male and white, reinforcing an impression that this end of the creative industries is not open to everybody.

Quotas and audits are often uncomfortable, leading to cries of tokenism or positive-discrimination. Yet the work of BAM, and the subtle and intriguing combinations of work that it has provoked in Speech Acts shows how by forcing the issue, important, engaging and previously unseen connections and ideas may be allowed to come to the surface. Only by questioning everything – from our systems of collecting and display to who we allow to talk about art, design and culture – will new voices be allowed to rise.

Speech Acts is on show at Manchester Art Gallery until April 22, 2019; manchesterartgallery.org