In the storytelling art-forms, there's a strong and proper convention that critics shouldn't give away endings and, since the multiplication of online reaction, that warnings about spoilers should be given.

Two London venues – the Royal Court and the National Theatre – have, though, recently gone further and tried to keep quiet the entire content of a play until audiences were able to see it. In the cases of both Joe Penhall's Birthday, opening at the Court next week, and Alan Bennett's People, scheduled to premiere at the National in late autumn, the theatres announced only the titles of the pieces, deliberately withholding plot details.

With the Penhall play, the reason was that the play is, in more than one sense, a concept piece: set in a maternity ward and beginning with a startling, physically impossible visual image. Late last year, when I interviewed Penhall for the Guardian about a previous play at the Court, Haunted Child, I was allowed to read Birthday as well, but only on the understanding that its central premise would be protected. It was also intended that advance marketing and posters for the production would be deliberately vague.

The National's reticence over the nature of the new Alan Bennett play may also be protecting an aspect of the plot or staging, but it represents a philosophical position adopted by the playwright and his director, Sir Nicholas Hytner. "The fantasy is that we can simply open it as a play and people come without knowing very much about it," he said, when announcing the play in January.

Bennett and Hytner seem to have felt, in common with many other creative professionals, that the intensive multimedia publicity business is increasingly disabling two of the most powerful tactics of narrative art: surprise and suspense. In cinema, which employs substantial trailers over several months as an advertising tactic, it is now almost impossible to buy a ticket for a film without knowing that this is the one in which Emily Blunt struggles to get married, or Bruce Willis plays a bookmaker. Such foreknowledge – which may, with heavily puffed products, extend to choice one-liners and even late plot-twists – is clearly an impure way of experiencing a story, and Hytner dreams of avoiding it in theatre.

The experience of the Royal Court, though, suggests that the director's hope for an unknowing opening of the Bennett may indeed remain a "fantasy". Theatre is a chatty business and, in order to stage a play, it is necessary for the script to be circulated among creative collaborators and shown to auditioning actors who, in some cases, may not have got the job but did get the gist of the script. Narrative security is even harder in a culture where performers and others are likely to tweet or blog. As it happens, the blackout on the Penhall play was first breached by an actor who posted a plot summary on Twitter during rehearsals. Her tweet was deleted but then the lead actor, Stephen Mangan, gave a newspaper interview, which proved impossible to conduct without addressing the conceit of the play.

So, if you still want to reach your seat at the Royal Court without knowing, look away, as they say during the football results on TV, for the duration of this paragraph. In Birthday, Mangan plays a gynaecological pioneer: a man who, following surgical and hormonal treatment, is able to give birth to a child.

Welcome back to incurious purists. Even if Penhall's secret had held, only a few preview audiences (and only the members of those who avoid online theatre news sites) would have watched the play in the state of perfect ignorance favoured by the dramatist. Once the reviewers come in, secrecy goes out, as critics can hardly be asked to suppress the beginning and middle of a play, as they are famously asked to keep quiet about the ending of The Mousetrap.

The biggest difficulty in putting a D-notice on a theatre production is that the script will often have a separate existence. David Hare, another playwright who dreams of audiences seeing plays without prejudice, has on some occasions refused to discuss the contents of new pieces in advance; a strategy wrecked when the published text was available in bookshops long before opening night.

Alan Bennett seems to have done his best to close off that supply route; although People appears in the Faber catalogue, there is, unusually, no plot description or commentary on the contents.

Even so, it would require a lot of luck to reach the first night without an actor, reader or audience member giving away whatever the game is. It is an admirable and understandable ambition for theatre to be seen without preconceptions; there is a particular thrill in literally having no idea what is coming next. But in a collaborative medium, secrecy is almost impossible, with the result that the advertising campaign for Birthday was doomed to be misconceived and People will have to rely on people being unusually discreet.