Nation's finest on display at British Art Show

• The Body and Ground (Or Your Lovely Smile) by Alexander Newton

YOU don't expect the curators of a major contemporary art show to start talking about the Bayeux Tapestry. But when I meet Tom Morton and Lisa Le Feuvre, the duo behind British Art Show 7, we quickly find ourselves discussing medieval needlecraft.

They're particularly interested that the tapestry, which shows William the Conqueror's victory at Hastings in 1066, also shows Halley's Comet, whose 75-76-year orbit means it has recurred at certain key moments in our history. Its last appearance, in 1986, was in the year of Margaret Thatcher's deregulation of the banks, says Morton, "to some degree the author of our present woes". The British Art Show (BAS) recurs every five years, and for the first time in its 35-year history it has a subtitle: In the Days of the Comet.

It remains the most important survey of contemporary art in Britain. Its touring exhibition visits various cities – this time round, Nottingham, London, Glasgow and Plymouth – aiming to explore the important developments in art in the previous five years. It's a tall order, and previous shows have been deemed to have varying rates of success. Le Feuvre, head of Sculpture Studies at the Henry Moore Institute, and Morton, a curator at the Hayward Gallery in London, were encouraged to find their own way to approach the brief.

"We set a few ground rules," says Le Feuvre. "One was that we would be in complete agreement with every single artist in the BAS. A second ground rule was that the starting point was always the art work, it wasn't about fulfilling criteria, whether that's about medium or age or anything else. And thirdly, we had a test for every single artist's work, that there was a real urgency to think about it at this moment, now. By setting these three parameters for the selection, it fell into place very easily."

One of the striking features of the show is the broad range of ways in which the 39 artists (or collaborations) work. There are figurative painters such as Michael Fullerton and Alasdair Gray; abstract painters such as Phoebe Unwin; sculpture by Sarah Lucas and Karla Black (who represents Scotland at the Venice Biennale next month); films by Luke Fowler and the Otolith Group; others who work across disciplines – Charles Avery, Roger Hiorns, Spartacus Chetwynd.

The BAS is in Glasgow for the first time since it was European City of Culture in 1990, showing in three venues: CCA, GoMA and Tramway. Le Feuvre says its return to Glasgow is vital, particularly given that one third of the artists in the show have lived, studied or worked here. "Britain has two centres for contemporary art, London and Glasgow. They set the tone for Britain being such an international centre for contemporary art. It's so important for us to be coming to Glasgow with this show."

They are committed to making a new show in each city, and including new work each time. In Glasgow, there will be new paintings by Unwin, a previous unseen sculpture by Keith Wilson and a performance work by Hiorns featuring a Glasgow boys' choir. Others artists, such as Karla Black and Charles Avery, will reconfigure their work. Avery has been to Mull (where he grew up) to fetch sand for his sculptural vitrine. Each time the show moves city, the curators explore new ways in which the works relate to one another. "This is not 39 separate solo shows, which is one way of doing an exhibition like this," says Morton. "We want to create an area where these works come together, get on each other's nerves, seduce each other."

It is crucial to this version of the BAS that it is not static, that there is "a certain dynamism, a certain refusal to settle". Le Feuvre says: "It's really important to us that it reflects the complicated-ness of making artwork, it's changing, it's testing ideas, it's never definitive. We're really interested in BAS proposing ways of thinking rather than claiming a new movement or claiming any truths. This show isn't telling us anything, it's proposing a way of thinking about how art operates in the world."

That is a world which is markedly different to five years ago. If it doesn't seem long since the last BAS in 2005, consider some of the changes worldwide: Barack Obama in the White House, the fall of New Labour, the global recession, the upsurge of change in the Middle East. Morton says: "In many cases, there are artists in the show making work it would be impossible to imagine being made in the last British Art Show. Matthew Darbyshire's installation (a room-shaped collection of kitsch consumer objects) is saying something about the deathknells of Blairite Britain, the dawning of Cameron's Britain, how the high street dealt with recession. It's impossible to imagine that work being made in 2005, with the confidence and ebullience there was then."

The age range of artists in the show is also broad, from Tris Vonna-Michell, in his twenties, to Alasdair Gray, in his seventies (both Glasgow School of Art graduates). The show also includes artists such as Sarah Lucas, who first came to recognition in the Young British Artists (YBA) movement of the early 1990s, and Wolfgang Tillmans, who won the Turner in 2000, but whom Morton and Le Feuvre believe are now making their best work.

As the "comet" subtitle suggests, many of the works deal with time and recurrence: Christian Marclay's 24-hour-long film The Clock functions both as a compelling collection of clips in which the time is mentioned and as a working timepiece; painter George Shaw revisits the landscapes in which he grew up in suburban Coventry; Olivia Plender (herself a fiction) investigates the archive of a fictional film-maker; Duncan Campbell looks at the ways in which TV portrayed young Irish radical Bernadette Devlin.

Alasdair Gray was an obvious choice, both curators say, because of the way he embraces time. "We were particularly interested in Alasdair's habit of beginning a drawing decades ago, say 1976, and finishing it decades later, and his announcement of this on the paper," says Morton. "One can almost imagine this as an Einstein-Rosen bridge, a kind of wormhole between two points in time."

Gray's work is also in the process of being "revisited" by the art world. Le Feuvre adds: "Although he has been making work for years, now is the time to think about his work in relation to what artists are thinking and doing and making. It's as if the whole world of the past, present and future are in these drawings."

If BAS 7 captures a shift in the way art is being made, it is a shift away from the generic "installation", which ousts traditional forms of sculpture, painting and filmmaking. Many of the artists in this show work in these forms, often with a high degree of skill, but in very contemporary ways. There is a new confidence, perhaps, in the ability of these forms to carry conceptual ideas.

Le Feuvre says: "The mid 1960s was the moment when art shifted from object to idea, and this is something which has permeated art-making since that time. Now, whether you're a specialist or a generalist in terms of engaging with art, you understand that artwork is conceptual in some way, it's ideas-generated, it's not about producing pictures of the world. It seems to me that over the last five years there's been a significant shift that takes that idea-driven conceptual practice and reconfigures it within a set of sculptures, paintings and films."

Both curators warn that some of the work in the show is challenging. "We're not interested in artwork being something that's easy and comfortable; completely the opposite," says Le Feuvre.

"We're interested in making an exhibition that makes the world slightly more complicated than it was before. It's about encouraging people to think deeper, look harder, and challenge their assumptions and expectations.

"Everyone alive today is an expert in the contemporary, so everyone is an expert in art being made today. It's as simple – and as difficult – as that."

• British Art Show 7: In the Days of the Comet is at the CCA, Gallery of Modern Art and Tramway, Glasgow, from 27 May until 21 August. For more see www.britishartshow.co.uk