LONDON — As a frequent visitor to the British Museum, I can attest that its vast Great Court has never been as full of Muslims — declaring themselves through headscarves, skull caps and prayer beads — as it is these days. They are swarming the museum to visit “Hajj: Journey to the Heart of Islam,’’ the first-ever exhibit about the annual Muslim pilgrimage to Mecca in Saudi Arabia. More than 80,000 people visited the exhibit in its first seven weeks. Moreover, it has fueled a much-needed dialogue about Islam in Britain, and demonstrated that cultural venues are well suited to host the difficult debate about multiculturalism.

The museum’s spherical reading room has been transformed with a life-size replica of the Kaaba, the structure at the center of the rituals in Mecca. The replica is adorned with sitaras, beautifully embroidered silk curtains that hang in the real Kaaba, and is surrounded by maps and archeological objects tracking historical pilgrim routes to Mecca from far-flung places like Timbuktu and Malaysia.

The artifacts that enliven the displays — illustrated manuscripts, maps, milestones, astrolabes developed to calculate the direction of Mecca, and plane tickets — reiterate both the commitment of Muslims over the centuries to fulfilling their religious obligations and the political reality that control over the holy sites in Saudi Arabia has long been synonymous with control over the Muslim world.

Since the Hajj exhibit began, the British Museum has been praised for fostering cultural diplomacy, acknowledging the role of Islam in British public life, and attracting new audiences to a cultural venue. In addition to tracing the history of the pilgrimage, the exhibit explains the purpose of the Hajj in Islam and the Muslim beliefs that inform the many rituals. The exhibit’s curators emphasize the attempt to highlight the spiritual aspects of Islam that are lost in frequent news headlines about terrorism and wars in Muslim countries.

Despite being surrounded by over 200 treasures and tapestries, I was certainly more fascinated by the diverse exhibition-goers and their varying levels of engagement with the faith itself: an elderly Muslim woman  gazed at pictures of Mecca, quietly crying to herself; bearded teenagers snickered at the odd perspective of ancient manuscript illustrations; a father bored his son with lofty tales of his own Hajj experience.

Amidst the praise, critics have also condemned the British Museum for perpetuating the foundation myths of Islam and permitting censorship under the guise of patronage: The exhibit has been organized in partnership with Saudi Arabia’s King Abdulaziz Public Library and thus presents a sanitized version of the Hajj. There is no mention of sectarian disputes, catastrophes like fires and stampedes that have killed hundreds of pilgrims in recent years, or the 1979 siege by Muslim terrorists of the Grand Mosque that houses the Kaaba.

Such criticism fails to view the Hajj exhibit in the broader context. In the same week that I visited the exhibit, I saw the theater company DV8’s “Can We Talk About This?’’ at the National Theatre, across the Thames from the British Museum.

This confrontational piece of “physical verbatim theater’’ criticizes British multiculturalism, forcefully arguing that political correctness has made it impossible to speak against militant, misogynist and extremist interpretations of Islam. By cataloguing instances of violence against critics of Islam like  Salman Rushdie and Ayaan Hirsi Ali, without acknowledging the daily, nonviolent practice of the religion by millions of Muslims around the world, the show walks a tightrope  — by its own admission — between argument and Islamophobia.

As a Pakistani visiting Britain, I am used to living in an Islamic republic where religion shapes every aspect of life and work, but discourse about the religion’s history and theology is endangered. For me, the specific content of the Hajj exhibit and DV8’s play is less interesting than the fact that they ran concurrently in London. As British policymakers struggle to answer the Muslim question — how the state should engage with Muslim citizens — cultural platforms are engaged in a lively, provocative and inclusive debate on Islam’s role in Britain.

What better venue for such a debate than one that privileges reflection and empathy over violence and discrimination?