“Goodnight, sweet prince,” Horatio says at the end of Hamlet, “and flights of angels sing thee to thy rest.” Not if the self-styled “Cumberbitches” have anything to do with it, he won’t. Such has been the racket they make at the stage door of London’s Barbican Theatre when the eponymous prince—a.k.a. actor Benedict Cumberbatch—appears after the show that authorities introduced a curfew following complaints from local residents. The general excitement outside the theater really has to be seen to be believed. When I attended in August, scores of (mostly) young people were sleeping rough outside the theater, queuing for the following morning’s “rush” tickets. Those looking for returns formed another long line. Fans already in place thronged the stage door, awaiting autographs and selfies after the three-hour performance.

The British press lapped up every moment to enliven the summer months. So we witnessed not just the row over Cumberbatch signing autographs, but the earlier one when he said he wouldn’t do any signings at all, along with his annoyance at fans using camera phones in the auditorium; his speech from the stage asking everyone to help Syrian refugees; and his outrage when The Times broke with tradition by printing a review before opening night.

Of course, all the excitement and press interest is due to the fact that Cumberbatch is a Hollywood Star, not just a thesp. Indeed, he is part of the shift in the last decade or so that has seen film stars regularly tread the boards in high-profile shows in London and New York. Many of the performances have been excellent (Jake Gyllenhaal in “Constellations”); some not so much (Maggie Gyllenhaal in “The Real Thing”). But few would deny that Hollywood’s pulling power has helped make theater more profitable, allowing venues to upgrade their facilities, even if some critics complain it has also made producers more conservative.

American audiences will have their own chance to see what the current fuss is about next week when Hamlet is broadcast in selected cinemas throughout the country. So what to expect? Let’s get the bad news over with first: in truth, this is not a great production. Es Devlin’s set, grandly magnificent as Elsinore castle in the first half, inexplicably becomes an earthquake zone in the second half—a fact that none of the actors refer to in words or gesture. Lyndsey Turner’s direction of a so-so cast is mostly plodding, and it seems an odd decision to have put a leading actor without much background in Shakespeare in the hands of a director with little or none. Cumberbatch would have been better-served, and better-tested, by the likes of Greg Doran at the Royal Shakespeare Company (RSC) or Dominic Dromgoole at the Globe Theatre. There’s an inevitable whiff of a vanity project here, including the fact that the just-above-average-height Cumberbatch appears to tower over everyone else on stage. Even the most eye-catching aspect of the production—the slow-motion action during Hamlet’s early soliloquies—is an obvious nod towards the actor’s role in the TV show, “Sherlock.”

And yet for all the faults of the production, Cumberbatch’s Hamlet is worth seeing. His Dane is essentially a grief-stricken, decent, rational man caught up, to quote Shakespeare’s contemporary Thomas Hobbes, in a life that is “nasty, brutish, and short.” On the central question of whether Hamlet is actually mad or playing mad, there is never any doubt that Cumberbatch’s prince is acting out a part. He emphasizes this essential rationality through clarity of diction. So while he does not stress the iambic pentameter of the verse, his clearly enunciated speech brings meaning to every phrase in a way that suggests a genuine immersion in the nuances of the text. There is some occasional gurning (for example, as a toy soldier in a toy castle), but we find his ultimate destruction moving because it is that of a good man outmaneuvered by a bad world.

That sense of a prince in need of The Prince worked for me, not least because it chimes with the RSC production that I saw as a boy in the same theater exactly thirty years ago. There’s a certain serendipitous poignancy in this fact, for Hamlet that night was played by Roger Rees, who died a few weeks before this current production began. Rees also played Hamlet as an innocent abroad in a brutal world, although with the larger-than-life Brian Blessed as Claudius, the contrast between the two worlds was even starker. Like Cumberbatch, Rees drew mixed reviews for his Hamlet, but I found the “clash of civilizations” between his foppish romanticism and the loutish violence of the new regime exhilarating.

It’s a similar sense of connection that will make Benedict Cumberbatch’s Hamlet culturally significant. The year I saw Roger Rees as Hamlet, I also saw Kenneth Branagh as Henry V and Antony Sher as Richard III—the leading roles that cemented the reputations of both actors. Sher’s performance still ranks as the most important performance of any play that I have ever seen. All three productions took Shakespeare away from set texts and the classroom, and elevated it to something real. Indeed, I owe my eagerness to see Hamlet this summer to the performances I saw all those summers ago. And although I found this production in some ways underpowered, the predominantly young audience clearly did not. They matched their commotion outside the theater with rapt attention and a standing ovation inside it. So ultimately “the play’s the thing.” If a star like Benedict Cumberbatch brings people to see Shakespeare, then he and they should be applauded for it. That’s as true in 2015 as it was in 1985. So you go for it, Cumberbitches!

“Hamlet” is broadcast in cinemas from October 15, 2015. For details, see the National Theatre’s website.