As readers rapidly come to suspect, critics tend to have their prejudices. After a period of exposure to most reviewers, it becomes relatively easy to predict what their broad reaction might be to, for example, a musical or to a new play dealing with religion or American foreign policy. So it is pleasing – and slightly surprising – to report that I seem to be overcoming a long-held theatre-going phobia.

My strong preference has always been for plays that take place in a theatre and feature words being spoken. This may sound like a political correspondent saying that he enjoys writing about Old Etonians plotting against each other, but there has been an increasing trend in recent years towards site-specific (a show taking place in a car park or even a car) and non-text-based shows, through the work of groups who specialise in "immersive" entertainments, including theatre company Punchdrunk and visual art outfits such as Artangel. On a bad day at the Edinburgh or Manchester festivals, there were times when a critic felt dizzy nostalgia at the sight of a seat or a script.

This conversion process – although, like Graham Greene's Catholicism, it is still riddled with doubts – was completed on Holkham Beach in Norfolk earlier this month. As part of the Norfolk & Norwich festival and London 2012, the American director, Robert Wilson, brought to the British coastline a piece he had previously staged in the Netherlands: Walking.

The game of golf was famously described as "a good walk spoiled" and Wilson's concept in this piece might be summarised as a pleasant stroll artistically directed. Groups of 19 ticket-holders reported to a hut in the Holkham Beach car park, where we were asked by supervisors in yellow cagoules to "surrender time to us", a command translated as the handing over of watches, mobile phones and cameras.

At that moment, my pretension-detector – the device that had always held me back from enjoying theatre of this kind – started to bleep and was still resounding as we were despatched in single file at 90-second intervals through a field to pass through a darkened room and then stand for several minutes within a willow-fenced enclosure while gazing down into a dark conical hole in the ground.

My guess – the main mental process in textless theatre – was that this stage represented a detoxification chamber and it seemed to work because my negative feelings about ambulatory site-specific pieces were noticeably fewer as one of the yellow jackets coached us in the agonisingly slow walking pace that we were required to follow during a three-hour trek through meadows, woods and sand-dunes before standing on the beach at Holkham and being lowered on wooden sacrificial slabs into a horizontal position, from which we meditated on sky and sea.

As the event ended, the familiar, mocking critical voice cut in, objecting to the frequent bossiness of practitioners such as Wilson (keep in step, and at this pace) and the easy borrowings from meditative religion and rehab. Could this really be called theatre in the way that Mark Rylance in Jez Butterworth's Jerusalem is? And yet, at the time and even now two weeks later, I remember and am affected by Walking – and especially the way in which it played with the pace of performance and thought – at a level rare in the majority of text-based shows.

On reflection, Wilson's piece completed a transformation in my attitude to the genre that had begun in 2009 with Punchdrunk's collaboration with Adam Curtis and Damon Albarn at the 2009 Manchester International Festival. For It Felt Like a Kiss, Felix Barrett's company took over a multi-storey office block in the city. The viewer walked through a labyrinth of installations, video and live action (an ambush by a running man with a chainsaw) related to paranoia and mind control. The changing of my mind was also helped by two interactive installations curated by Artangel, in which participants also wandered through empty premises filled with spooky interventions: Gregor Schneider's Die Familie Schneider (2004) and Ryan Gander's Locked Room Scenario (2011).

With the zeal of any convert, I now see that the power of this form is that the viewer is in control of the narrative (although this can also happen with clever text pieces such as Martin Crimp's Dealing with Clair and Caryl Churchill's Love and Information) and that the story takes on ambiguities unlikely in a traditional venue. In Wilson's Walking, is that woman with a dog part of the event or just a pet-owner strolling? The climax of Gander's Locked Room Scenario was what at first seemed to be an accidental collision with a pedestrian in the street after leaving the building.

My continuing concern about the genre is that many examples of immersive drama and artwork against the idea of a shared experience – the traditional definition of theatre – in favour of individual exposure, as if in some humanised videogame. In Walking, each participant was deliberately isolated throughout, while It Felt Like a Kiss, Die Familie Schneider and Locked Room Scenario all required ticket-holders to go in alone. Because of the tiny numbers that can be accommodated, such projects inevitably become elitist. Robert Wilson, though, has got me walking in step at least part of the way.