At the British Museum, Nazia Shah, 27, had embarked on a day out from Luton with half a dozen of her nephews. They fancied a theme park, but she took them to see Hajj: Journey to the Heart of Islam before it closes .

But they looked far from despondent. "It's good for the kids to get in contact with a bit of history and for them to know what's going on in the world," she said. A veteran of the pilgrimage to Mecca, the only thing she felt the exhibition lacked was a model of the Jamarat, the pillars stoned by the faithful. Next stop was the Natural History Museum – "to tire them out properly."

Shah is one of an estimated 60,000 British Muslims who have visited the Hajj exhibition since it opened in January. The first museum show anywhere in the world to focus on the pilgrimage, in less than seven weeks it exceeded the museum's target of 80,000 visitors.

By the end of last Sunday, 119,948 adult tickets (under-16s get in free) had been sold at £12 each, with all advance tickets sold out and the museum opening for longer hours to accommodate the extra demand.

Though the museum does not monitor the religion of its visitors, director Neil MacGregor estimated that more than half were Muslim, an unprecedented number. "We've had groups coming in coaches from Birmingham, Manchester – all over the UK," said Qaisra Khan, the exhibition's project curator. "We're getting carloads of people. Just this morning a young girl tweeted me saying that nine family members came down from Bradford."

It's an impression borne out in the exhibition. "Our teachers were telling us about the show so we thought we'd get here as quickly as possible," said Hymayrah Hoqe, 11, one of a dozen girls from a group organised by the East London mosque.

Khan said the museum was surprised at how popular the show had been, although they had deliberately targeted Muslims over the two years it took to plan and market it.

First, Khan contacted Maqsood Ahmed, then senior adviser to Muslim communities in the Communities and Local Government department.

"He pulled together the umbrella organisations and groups around the UK who had a good reputation and were moderate, and who would understand what we were doing with the exhibition, take it to their congregation or members and post information on their sites."

The groups included the Council of British Hajjis and the Association of British Hujjaj, both of whom help organise the Hajj for British Muslims.

The museum also invited local Muslim community groups into previews of the show to create a word-of-mouth buzz. "Once one group is able to say 'we really recommend this' it spreads like wildfire," said Khan.

At the museum, the reaction from Muslims was strongly positive, though Malik, who had been on the Hajj, said it taught her little she did not already know.

The exhibition has been contentious, however, with commentators including the Observer's Nick Cohen claiming that it has been compromised by the involvement of the Saudi Arabian regime.

The state lent exhibits, including the seetanah, which covers the door of the Kaaba, while the exhibition is partnered with the King Abdulaziz Public Library and sponsored by the Islamic bank, HSBC Amanah.

Mehdi Hasan, who reviewed the show for the New Statesman and Radio 4, said he acclaimed the exhibition for being "something positive about Muslims in a country where all you get is terrorism and Halal meat scares", but believed many Muslims would have had mixed feelings. You want to like it but you don't want to feel part of a Saudi spin operation. Hajj takes place in Saudi Arabia, it's run by the Saudi government, and they use it to promulgate their narrow, very sectarian view of Islam."

Under the Wahabi monarchy, much of medieval Mecca was bulldozed with the justification that religious relics encouraged idolatry.

"They got away with zero criticism in the exhibition," said Hasan. "When you get to the section on King Abdulaziz, the founder of the Saudi state, you get a [text] about what a moderniser he was, like he was the Tony Blair of Saudi Arabia. This is a man who as soon as he arrived in Mecca was smashing stuff up, killing people and flattening tombs, and yet is presented as this guy who made the trains run on time.

"The British Museum is meant to be the great protector of global culture yet they've got nothing to say about the Saudi government tearing stuff down in Mecca and putting up hotel blocks and timeshares."

Hasan said the Saudis would be very pleased by the exhibition. "They've got a huge boost for the Hajj which they need in terms of cash revenue. In that sense, they've made a very direct connection with British Muslims."

The museum responded that the Saudis had "not contributed funds to this project or had any curatorial control over the content of the exhibition".

"I think most of our audiences recognised what we were trying to do, which was to display and demonstrate this very personal, spiritual journey," said Khan. "It wasn't about the politics of it."

Having tapped into a new audience of British Muslims, Khan said that while no further exhibitions along the lines of Hajj were planned, she was confident they would return to the British Museum, whose Islamic gallery is run by the show's curator, Venetia Porter.

Habib said she would return, and not just confine herself to the Islamic exhibits.

"As the kids are getting older they're doing Vikings and Egyptians at school so it's good to get back here."

"I've always been into museums," said Idil Yusuf, from south-east London, with daughter Jamila, three. "Now she's of a certain age I'll be able to bring her down with me."

The group from the East London mosque, meanwhile, already seemed au fait with the place. "We've all been here before," said Hoqe, "and we'll come back with our family."

• Correction 17/4: The piece wrongly stated that the Mahmal tent had been lent by the Saudi Arabian state. In fact it was lent by the Nasser D. Khalili Collection of Islamic Art. This has been corrected