The directions have led me to a military checkpoint underneath Waterloo station. Officials scrutinise my census paper, and I’m nodded through. A soldier reaches around his machinegun into his pocket, slips me a token and whispers “Free drinks for the French”. I’m not French, but I have come dressed as a smart European from the late 1950s (below-the-knee skirt and a foulard) to experience the latest event from Secret Cinema.

I was first tipped-off about Secret Cinema by a friend who had heard about it from a colleague; most attendees discover it through the grapevine. True to its name, it doesn’t advertise overtly, but has an understated website where you can register for information about forthcoming events and purchase tickets. Ever since a few hundred people gathered to watch “Paradise Park” one night in December 2007, Secret Cinema has snowballed. During a three-week run of screenings this spring (which ended last weekend), 12,000 attendees (including me) ended up descending on the Old Vic Tunnels for a mysterious cinematic adventure. In the past year Secret Cinema has held events in Berlin and New York, and organisers are scouting for locations in Rome.

Tickets are released about a month before the event, and sometimes sell out within hours. We buy them without knowing which film will be shown, or where, but they promise a unique experience: a screening (probably a cult classic) in a lively atmosphere that includes characters re-enacting scenes, thematic installations, related food and drink and some audience interaction. Events take place every couple of months, and each one is held in a different unknown location in London – a derelict theatre, a disused hospital, underground tunnels – revealed to ticket-buyers only days before. The company’s website is deliberately oblique, but it is the gateway to a lively presence across social media, where organisers plant clues and fans try to guess the next film.

This time round we received e-mails a week or so before, addressed to “citizens” from the “state”. We were told to fill out our census paper and “Remain strong. Remain united”. As the event drew closer, further clues about the film were drip-fed through cryptic quotes and links on Facebook and Twitter (such as, “Are you ready citizens? http://bit.ly/mPzVuj”). Organisers also linked to Radio Noir, an online radio station playing nostalgic 1950s tunes, created especially for this event. Speculation, hearsay and anticipation make for a perfect recipe for buzz. The company’s oft-reiterated tagline, “Tell No-One”, instantly taps our tendency towards gossip. Fabien Riggall, the founder of Secret Cinema, assures me their events are for all ages. But this social-network based approach tends to attract a youthful, web-savvy crowd.

After passing the checkpoint I explore the location. I duck under a washing line to enter the Casbah, where there is a mosque, a silent prayer room and the smell of lamb kebabs in the air. There is a constant murmur in Arabic and the occasional gunshot. At the back sits a Parisian café with a chic bar and smart waiters. Further exploration reveals a chicken-wire prison, where a French soldier mock-tortures an Algerian prisoner. Among some 500 quizzical ticket-holders, I overhear exclamations of “What’s that?” and “Where are we?” Others smugly tell their friends, “I’ve guessed it”.

As I wander the Casbah, a white-smocked lady leads me into a room to watch a traditional marriage ceremony. Then there is an explosion in the bar, and a flurry of actors and surprised cinephiles burst round the corner as soldiers step in to control the crowd. These performances are choreographed to encourage excitement and spontaneous involvement from the audience. Riggall says he is “very interested in the blur between the audience and the performer”. He suggests the attendees have the biggest role to play.

After a couple of hours of frolic and guesswork, we are shepherded into screening rooms to watch the film. As the credits role the secret is revealed: we will be watching “The Battle of Algiers”, Gillo Pontecorvo’s 1966 film about the struggle for liberation from the French, which some have described as one of the greatest political films ever made.

For Riggall, Secret Cinema is an alternative to the lamentable experience of the multiplex. Yet his ambitious events are in danger of sacrificing film appreciation to spectacle. We watched “The Battle of Algiers” on a medium-sized screen with the occasional chatter of people in the bar next-door, partitioned off with merely a velvet curtain across a doorway. Those who prefer a cinema experience of luxury seats, surround-sound and a panoramic screen should look elsewhere. The appeal of Secret Cinema is in the full event, from giddy mystery to tipsy denouement.

As the director of Future Shorts, a company that has been producing and distributing short films since 2003, Riggall sees film as a useful medium for inspiring dialogue and debate. He says he chose “The Battle of Algiers” for the way it resonates with contemporary stories of unrest, particularly in the Arab world. Audiences want to be entertained, he says, but they also want something that makes them think. A thrill creeps into his voice as he describes seeing two middle-aged ladies dressed as Algerians in the bomb-maker’s house, scarves tied rebel-like round their heads, nodding intently to the man’s Arabic instructions.

Although not always political, Secret Cinema is certainly an immersive experience. Past themes have included our treatment of the insane (“One Flew Over the Cuckoo’s Nest”) and the future of the planet (“Blade Runner”). The result is a transporting bit of escapism, but also surprisingly provocative.

Riggall has some ambitious ideas for future events, including somehow screening “Catch Me If You Can” on a Virgin Atlantic flight. Time will tell whether Secret Cinema sustains is popularity, but Riggall seems game for the challenge. “There are no rules because it is a secret,” he says. “We can do anything.”