For those who haven't been to Bradford's Cartwright Hall Art Gallery, here's a bit of essential background. It sits in a beautifully laid out and maintained public park on a hillside overlooking the once-flourishing textile city. At the time of its early 20th-century opening, the area was evidently one of solid middle-class prosperity and aspiration.

Just as the planting in the surrounding Lister Park was intended from the outset to instruct as well as to delight, so the early collecting of the museum service, founded in 1879, was clearly directed both towards giving Bradford's citizens a sense of pride in local manufacturing achievements and to enriching their lives via exposure to the fine and decorative arts. So far so good and, indeed, so unremarkable in its time.

But in the century since Cartwright Hall's opening, Bradford has arguably experienced greater demographic and economic shifts than almost any other UK city, and that's the gallery's challenge.

It now sits in an area of considerable ethnic and social diversity and the textile trade that once linked Bradford to the world has vanished. Today, the world is linked to Bradford by the cultures of its citizens, and it's those citizens that the Connect galleries, which opened late last year, seek to attract and reflect.

New demographics

To some extent, the museum service was ahead of the game as a result of some judicious collecting and commissioning in the latter decades of the last century, which has been further enriched by more recent project-led acquisition. But it's not having the stuff that matters; it's what you do with it. So what have they done with it?

Connect occupies the entire first floor of the building, with the ground floor devoted mainly to circulation and temporary exhibition areas. Once at the top of the grand staircase, the thematic layout of People, Place and Imagination is fairly clearly articulated, although there was the odd instance where I found myself wondering why a work was "here" and not "there".

As someone who is always deeply resistant to information-heavy top down didactic displays, I was encouraged by the exhortation to "connect different objects in these galleries. Search for the connections yourself or let us guide you". So although friendly staff had been quick to ensure I had a copy of the excellent accompanying booklet, I chose not to use it as a guide and set out to search for my own connections.

Only connect

If I had to confine this review to a single phrase, it would be "light touch". Nothing is forced down the visitor's throat, there's no politically correct tub-thumping, hardly a questionable enforced relationship, and no pressure to see things in anything other than one's own way. That said, there's some great support if you want it. This comes in the form of touchscreens and clear but unpatronising text.

Most of the impact - and most of the connection - is achieved through the gallery layout and the thoughtful and occasionally brilliant hang. At a time when so many provincial art galleries seem to feel they must reinvent themselves as social history museums, Cartwright Hall remains emphatically and wonderfully an art gallery. But it's an art gallery with its eye clearly on its own confidently identified 21st-century audiences.

In addition to the overarching "headline" topics, different sub-themes and groups of works suggest commonalities of experience. In a corner in the Place gallery Sylvat Aziz's disturbing 1993 Exodus Lahore, primarily a response to the horrors of the 1947 partition, is hung with Polish artist Edward Dwurnik's 1978 lithograph Violence in Town and Graham Sutherland's 1941 compulsorily unpeopled account of the demolition of a bombed building. It's hard not to connect.

In Imagination, the fine, decorative and applied arts illustrate ways in which makers from different cultures have responded to the potential and limitations of materials. So in a case of glass we're invited to connect a Syrian mosque lamp with one made locally in Bradford, while in the silver case Rajesh Gogna's Contemporary Hookah was made in 2001 as a response to one already in the Bradford collections.

In the same gallery, Bradford's connection with David Hockney is represented by Le Plongeur. Inevitably, where large 19th-century canvases have been included, they tend to dominate because of their sheer size, but then there are also works such as Peter Sanders' 2001 photograph, The Mystery of the Kabbah, which can more than match them in terms of impact.

In some ways, the People gallery was for me the least successful, not least because much of what was relevant there might easily have been in one of the other galleries instead, and sometimes was. Charles Staniland's The Emigrant Ship, was in Place, when to me it spoke most loudly of people, as did Yinka Shonibare's moving Wanderer.

That said, this was probably the most difficult theme to pull together in terms of curatorial decision making and here, as elsewhere, there are some lovely moments.

A corner for couples brings together Joshua Reynolds's John, second Earl of Elmont and his Second Wife, Catherine, GF Watt's Paolo and Francesca and Chris Ofili's Afro-Lunar Lovers II; elsewhere Andy Warhol's Marilyn is hung close to a Hollywood film poster.

There are weaknesses, but the overall subtlety and restraint of the project impress enormously. The most meaningful connections have to be made by the people of Bradford and they really seem to be making them.

Nichola Johnson is the director of the Sainsbury Centre for Visual Arts in Norwich
Project data

Cost: £1.97m
Main funders: Heritage Lottery Fund £1m, Arts Council England, Renaissance Yorkshire, Alchemy, DCMS/Wolfson Foundation Museums and Galleries Improvement Funds, Friends of Bradford Art Galleries & Museums, Calouste Gulbenkian Foundation, Idlewild Trust
Exhibition design: Redman
Fit out: Wood Mitchell
Display cases: Armour Systems
Interactives Paragon
AV hardware: Black Box
AV production: Centrescreen
Lighting design: Paul Ruffles
Lighting hardware: Concord
Graphics production: Leech
Mounting: Dauphin
Quantity surveyor: S Rex Proctor
Specialist blinds: Dearnley's