To find the most romantic spot in Romeo and Juliet's home city of Verona, you must take a dual carriageway out of the picturesque centre, then turn down a ramp into a decrepit industrial estate. Beyond the cemetery, next to a railway siding, is an office whose stock-in-trade is people's most passionately guarded secrets, their deepest hopes and fears. The headquarters of the Club di Giulietta (Juliet's Club) is also the inspiration for a soon-to-be-released movie.

Letters To Juliet tells the fictional story of a young American journalist who has joined this remarkable group of volunteers, replying to messages sent from all over the globe to Shakespeare's heroine by lovers seeking advice, or an excuse to unburden themselves. Sitting around a table strewn with handwritten letters, three of Juliet's real "secretaries", Giovanna Tamassia, Elena Marchi and Gioia Ambrosi, tell stories that are by turns touching and weird, thought-provoking and heart-rending.

"It's a great responsibility," says Tamassia, whose father Giulio is the club's president and a founder member. Ambrosi, a 25-year-old student and the closest approximation to the heroine of Letters to Juliet (played by Amanda Seyfried), describes the correspondence as "a blog on humanity".

The film puts Juliet's secretaries in an office overlooking the balcony of the house where it is claimed Shakespeare's heroine lived. While the club has an outpost there, the real work is done by 15 unpaid people in this little red-brick office next to the railway tracks.

As far as anyone knows, the first letter, addressed simply to "Juliet, Verona", arrived in the 1930s, probably as the result of George Cukor's film version of Shakespeare's tragedy. The letter found its way to "Juliet's tomb", another location of dubious authenticity, in the crypt of a monastery just outside the city walls. The attendant there, a veteran who had picked up some English in the first world war, decided to reply. And he carried on replying as more letters arrived.

After the second world war, a local poet secretly took on the role of Juliet's secretary but gave it up, apparently in embarrassment, when his identity became known. Finally, in the 80s, the then mayor of Verona decided to give the task to the Club di Giulietta, a group formed to promote initiatives linking their city to the play.

"We get more than 5,000 letters a year," says Tamassia. "And then there are the thousands of notes that get left behind at Juliet's house and tomb."

She reckons about three-quarters of the messages are from women, and that the biggest single group is made up of American teenagers. On the wall of the arch leading to Juliet's house in the medieval centre of Verona, though, there are notes in every conceivable language: full-blown letters and professions of undying love from Hamid to Zineb, from Xona to Katrina, in Chinese and in Serbo-Croat. Some are genuinely poetic ("For hope and love; for the one I loved most, my lover, my heart," in French); others less so ("I've got a stomach ache in the heart," complains a less-than-usually romantic Italian).

Even in early May, there is a constant people-jam beneath the arch as visitors cram in and out of the supposed home of a fictional character. A notice tells visitors the house has been owned since the 1200s by a family called Capello, adding unequivocally that "from this derives the name Capuleti, the noble house of Juliet."

Juliet's house also has a postbox where letters can be left and four computer work stations, clad in mock-antique metal casings, where visitors may tap out a message to the girl who hung "upon the cheek of night like a rich jewel in an Ethiope's ear". But surprisingly, perhaps, emails account for fewer than 10% of the messages that end up in her secretaries' offices.

Of the letters, the vast majority are handwritten with pen and ink. And that is how they are always replied to. "What people often write is: 'You are the only one who can understand me'," says Giovanni Carabetta, the club's archivist.

Nigerian-born Franklin Ohenhn, who replaced his sister as one of Juliet's secretaries, says he sometimes finds himself drawn into worlds that are as far as it is possible to imagine from gentle, picturesque Verona. "One girl in the ninth grade told me she was crying as she wrote her letter, about a boyfriend who had been killed in a gang fight in the US." The most difficult letter he has dealt with was from another American teenager, who wanted to know if she should keep the baby of a boy she knew was playing around. "I told her to follow her heart," Ohenhn says with a shrug.

The secretaries can call on the services of a psychologist, and sometimes they need them. "I think the strangest case we have in the archives is one that concerns a young man from Verona," Tamassia says. "When he was 24 years old, he was in a cemetery and saw the photograph of a young woman on a tomb. She had been dead for decades, and the tomb was untended. He began to look after it and gradually formed a relationship with her. He lived it as if it were love."

"In the end, nothing seems strange to us," Tamassia adds. She can only remember one case in which the club decided not to reply to a letter. There was a period in which a number of American prison inmates wrote to Juliet, and one of them maintained a lengthy correspondence.

"He was someone with big problems in his life, and he told me all about them: his love for his girlfriend whom he had lost after being sent to prison; his relationship with his father who had beaten him. But then he became more and more insistent and, at a certain point, I got frightened. He was asking for our address. I decided to stop writing back," she says.

Perhaps the most extraordinary aspect of this whole endeavour is that the secretaries do it for free. "Well, the council gives us the money for the stamps," explains Giulio Tamassia. "But it's not even enough [to cover the postage]. Right now, I'm having a battle with the council. What we do brings all sorts of advantages for Verona, and I think it is time they stopped treating us like this. We're all working for nothing."

Carabetta smiles. "Not for nothing, Giulio . . . For the pleasure of reading these wonderful letters."

And perhaps, in some cases, for other, more personal reasons. "It has helped me to believe again in feelings," says Marchi. "If a love affair is happy, it is happy. But what counts is to have a heart that is alive, no? To be in touch with your feelings, however things go. It's not as if there is a guarantee as to the future."

A sentiment with which the real – or rather, fictional – Juliet would have fervently agreed.

• Letters to Juliet is released in the UK on June 9.