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The foyer of the Cottesloe at the National Theatre is buzzing when I arrive, as groups of disabled and non-disabled people bustle about, organising tickets and purchasing drinks. We are all here to see a dramatized version of Mark Haddon's highly successful 2003 book, The Curious Incident of the Dog in the Night-time.

The sell-out play tells the story of 15 year old Christopher Boone who has Asperger's syndrome, an autistic spectrum disorder. Those with the condition are typically high functioning, can have social difficulties and are often very sensitive to light and sounds.

The author of the original text did not have Asperger's and neither do any of the actors, but today, many in the audience have autism or a learning disability of some kind. I am at what's known as a "relaxed performance", which is summarised on the National Theatre's own website in a very friendly and inviting manner: "The atmosphere in the auditorium will be relaxed to provide a more supportive environment - a bit like the quiet carriage on the train ... but the opposite! Audience members will be free to come and go as they please throughout the performance and make noise if they want to."

Relaxed performances at other theatres have had a chill out room where people who need quiet time can go before, during or after the show. Some even relay the play on a big screen, so that if someone needs to leave the auditorium they can still follow the story. Today, the Cottesloe foyer has been designated as a quiet space.

Most relaxed performances so far have been for shows aimed at families with children who are learning disabled or on the autistic spectrum and who would otherwise be unable to go to the theatre. But The Curious Incident of the Dog in the Night-Time is pitched at those over the age of 13 and a notice on the website sensitively advises: "This play is most suitable for those who will enjoy a narrative-driven performance."

To prepare audience members with autism who find surprises uncomfortable, a letter was sent out in the weeks leading up to the performance. It reassuringly explains precisely what we can expect from the day, including at what time we can enter the auditorium, when the show will start, how long it will be and the length of the interval.

The play starts slightly later than billed but nobody seems to mind. This is The National Theatre's first attempt at a relaxed performance, so they can be forgiven for not realising how long it can take us disabled people to get seated ... particularly when travelling in large groups.

The show is in two parts, separated by an interval.

It takes a short while for the audience to settle down, and I wonder just how "relaxed" the audience might get.

The theatre is not silent but not hugely noisy either. Sometimes I can hear people talking quietly to each other or commenting on the action, at other moments a vocal tic or noise can be heard, and there is a constant gentle rustling, as people shuffle in their seats, move involuntarily or leave to take a toilet break. Instead of proving a problem, this underlying sound makes everything feel rather cosy and natural.

There is plenty of laughter. This is partly because the play is, at times, very funny but some audience members also laugh out loud when the actors use a swear word.

Possibly the most unusual occurrence in the auditorium is during a violent scene between Christopher and his father. A group of people laugh throughout a tense and dramatic moment which, I'd imagine, would ordinarily be met with silent horror.

It could be that this reaction is from a section of the audience struggling to understand what is happening on stage, however, all theatre-goers will have received "visual stories" or storyboards, a couple of weeks before this relaxed performance, so that they already know the narrative and feel prepared for each bit as it comes along.

For a group of people with autism and learning disabilities, a disabled person experiencing violence at the hand of a parent must have been frightening to see. In emotional moments, sometimes people laugh if they don't know how else to react.

I meet Anna Dragicevic at the interval. Like Christopher in the play, 19 year old Anna has Asperger's syndrome. She also has a diagnosis of ADHD.

She has seen The Curious Incident of the Dog in the Night-Time twice before and, although the performance hasn't been changed, she notes that some thoughtful minor tweaks in this relaxed version have left her much less tense.

"I notice that the sounds are a lot quieter. Loud sounds can put me off and take my attention away. I also have trouble sitting still and keeping quiet, so to be able to speak and to move around much more freely makes me feel better."

Many relaxed performances also make changes to a plays lighting, sometimes keeping the lights half up throughout. Today, some of the play's usual strobe lighting effects were tempered. Strobe lighting can cause problems for people with epilepsy.

The interval ends and the second half goes off without a hitch. So much so, that It is only when the play is over, that I realise how hard everyone has been concentrating on the performance. Even though moving and speaking was allowed, many had obviously been doing their best to stay still and quiet, because as soon as the curtain comes down and we are all wrenched back to reality, the people noise ramps up significantly.

I found this relaxed approach to The Curious Incident of the Dog in the Night-time genuinely enjoyable and in fact left the National Theatre wondering why theatre etiquette is so rigid and whether maybe, every performance should be a "relaxed performance".

• The Curious Incident of the Dog in the Night-Time is sold out but there are still tickets available for the on 27 October.

• Later this year, The Ambassador Theatre Group will be holding relaxed performances of three pantomimes, in Bromley, Grimsby and Richmond. If the pilot scheme is successful, ATG hopes to present a relaxed performance at one of its West End theatres in 2013.

Have you ever attended a relaxed performance? Tell us about it in the comments below.