Hamlet at the Barbican, which will star Benedict Cumberbatch over a 12-week run next summer, has become the most in-demand theatre production of all time, according to the ticket website Viagogo.

The production has became the most searched-for event on the ticketing site, with demand outstripping the popularity of the Young Vic's A Streetcar Named Desire, featuring Gillian Anderson – the next most popular play, by four to one. In the hours following the release of tickets, the popularity of the show also appeared to outstrip demand for major music tours, registering 214% more ticket searches than Beyoncé & Jay Z's On the Run tour.

Hamlet tickets went on sale at 10am on Monday and within minutes would-be buyers found themselves, according to some accounts, more than 20,000 places back in the queue. Advance tickets start at £30, but 100 seats priced at £10 are also available for each performance.

People took to Twitter to express both frustration and delight. Megan Frances wrote: "More people wanted tickets to see #HamletBarbican than Beyoncé ... #BenedictCumberbatch just outdid Queen Bey … Whoa."

Another user, Christina Bianco, having posted a screen grab showing the 26,000 people in front of her in the queue, wrote: "To those buying tix to see #BenedictCumberbatch in Hamlet today, we have QUITE a wait & maybe a fight ahead of us." A Cumberbatch fan with the Twitter handle @Allons_y_Holmes, wrote of the "torture" of waiting for tickets, but after securing a seat tweeted, in capitals: "I GET TO SEE MY GORGEOUS BENEDICT CUMBERBATCH NEXT YEAR IM CRYING."

The production, directed by Lyndsey Turner, best known for her work on Posh and Lucy Kirkwood's Chimerica in the West End, will have its premiere on 5 August and run until 31 October next year.