The Queen made a rare visit to a mosque yesterday, donning a headscarf alongside the wife of Turkey’s President to tour the crypt and caverns of an historic Islamic shrine.

It was also the first formal solo outing for Hayrünnisa Gül, the country’s controversial “first lady”, who accompanied the Queen around the Green Mosque and tomb of Sultan Mehmet I on the second day of the Queen’s state visit to Turkey.

Mrs Gül wore the full Turkish headscarf while the royal hairline was hidden by a piece of chiffon. Mrs Gül is the first presidential wife to wear the scarf, infuriating generals and establishment leaders desperate to maintain the nation’s secular character.

The Green Mosque is one of a tiny number to be visited by the Queen during her 55-year reign. The gesture will be appreciated by many in Turkey as the country, a secular state with a resolutely Muslim population, tries to persuade Western neighbours that Islam and EU membership can coexist.

“This sends an important message to the world,” Nurten Ilgrin, a heavy-set, headscarfed housewife, said of the two dignitaries observing religious rights together. “It makes me happy and proud, and it would be nice if leaders respected each other’s religions like this more often.” There was a tinge of disappointment, however. Mrs Ilgrin, who travelled to the northwestern city of Bursa for the visit, said: “I had hoped to see her crown.”

The Queen arrived in the courtyard of the mosque complex in a large, off-white hat. A small crowd whistled and clapped as the royal party disembarked but the mood was one of polite curiosity rather than fevered excitement. For the Queen’s first state visit in 1971, tens of thousands of Turks turned out. Abdullah Guler, 60, said: “We see famous people on the TV all the time nowadays so it’s less of an event than it was then.”

At the mosque entrance an aide in an embroidered robe knelt to assist the Queen as she struggled briefly to remove a shoe. She then donned slippers before entering. Imam Ayhan Polat showed her around the 15th-century complex, built while Bursa was still capital of the Ottoman Empire, taking time to point out the tiles that give the Green Mosque its name. As he chanted verses from the Koran, Mrs Gül and the Queen took their seats while the rest of the party knelt in prayer.

As the Queen explored minarets and a mausoleum, the Duke of Edinburgh took to the more prosaic task of visiting a car factory. Bursa used to be the last stop on the Silk Road. Now, it has a thriving economy based on car manufacturing – another aspect of Turkey that, it is hoped, will boost its credentials in Brussels.

Earlier the royal couple managed to squeeze in an event promoting women entrepreneurs, between art galleries and puppet shows. However, Gulay Ozdemir, a secretary passing by the mosque with her young daughters, said that she wished their visit had focused more on weightier issues affecting ordinary Turkish life rather than local arts and crafts. “It would have been better to use this opportunity to talk about important things like women’s rights, and the challenges facing divorced mothers like myself.”

She also lamented the lack of interaction with locals. “We have not seen the Queen much, which is a shame. She is welcome to come around to my house for a coffee any time.”

Soon after, the Queen emerged from the mosque. With her hat firmly back in place, it was off to another engagement to admire more ceramics. The royal party then departed for Istanbul, deaf to the sounds of a beautiful call to prayer.