It’s pretty luxurious to be able to stumble out of your front door at ten to six, wander five minutes round the corner to your friendly local cinema, be greeted with a glass of sparkling wine, and then watch a high-definition live screening of a top contemporary opera production at the Met. This Saturday night, which I spent watching Thomas Adès’ The Tempest at The Lexi Cinema, Kensal Rise in London, was by far the easiest night at the opera I’ve ever experienced, and as it turned out it was one of the most musically satisfying too, with the sort of almost inhumanly strong cast demanded by both this terrifically difficult work and the Met’s own standards.

Adès and librettist Meredith Oakes’ opera premièred at the Royal Opera House in 2004 and has already travelled widely, enjoying several productions. The Met’s new version comes courtesy of Robert Lepage, who has chosen to set this adaptation of Shakespeare’s play inside a 19th-century recreation of Milan’s La Scala opera house. This conceit, lighter in effect than it sounds, renews the focus on theatre and illusion which is present in Shakespeare’s original but lessened in Oakes’ effective but gnomic adaptation. There is plenty of room for visual thrills in this production, including some stage hands dressed all in black who deftly help Ariel fly, and the set and costume designs are also remarkable – the many tattoos of Prospero (Simon Keenlyside) in particular. Mostly, though, the visual and dramatic elements seemed subordinate to the musical content, which was spellbinding from first to last.

Anyone who doubts new classical music’s capacity to be lyrical, when it wants to be, would do well to give The Tempest a spin. Adès responds to this romantic, fanciful story with romantic and fanciful music. He is unafraid to be direct and emotive, as in Miranda and Ferdinand’s love duet and moments in Caliban’s part (most memorably his “strange noises” speech, which sounded a bit like Elgar at times), but it’s an intelligently contemporary piece as well, which plays out as a kind of quizzical commentary on the spectre of late-Romantic excess which continues to pervade the world’s opera houses. While that might sound too bookish, the opera itself doesn’t; it’s hard to think what more you could ask of a new operatic work, and especially one which takes on Shakespeare so directly.

Adès’ complete willingness to engage head-on with opera’s past finds its counterpart in Meredith Oakes’ remarkable text, which shows no qualms about fitting Shakespeare’s story and his language into a new and singer-friendly frame. Occasionally it borders on the rock-lyric trite (Caliban’s “You scorn me and you strike me / You say you do not like me” was a low point) but most of the time the libretto’s concision is admirable, and the way the plot is bent into shape is exemplary – much is expunged and the odd corner is cut, but it doesn’t come across as a simplification so much as a thoughtful reworking.

It’s hard to know where to start with the large and uniformly brilliant cast, though the two non-humans Ariel and Caliban do deserve particular mention. Ariel is an almost unbelievably high role for coloratura soprano, and Audrey Luna’s stratospheric performance met its demands perfectly. Caliban, on the other hand, was given an appropriately earthy, coarse performance by tenor Alan Oke in a furry suit. As Adès commented in a brief interview, it’s a role possible to interpret in many ways (the original Caliban was the completely different tenor Ian Bostridge), but Oke’s take on it had the right amount of heft.

Simon Keenlyside’s Prospero was immensely impressive. It’s a part described as for “high baritone” but it sounds at times more like a pure tenor role, and at others like a low-ish baritone one. With a huge amount of time on stage to compound the difficulty of the part, it’s not a role to tackle lightly, but a more compelling performance than Keenlyside’s is hard to imagine. While few of the other parts allow quite as much scope for virtuosity, there wasn’t a weak link among the singers: leads Alek Shrader (Ferdinand) and Isabel Leonard (Miranda) were a doe-eyed and endearing pair, as were drunkards Iestyn Davies (Trinculo) and Kevin Burdette (Stefano). Among the rest of the courtiers, most memorable were the lightly pompous lines of Toby Spence as the arrogant Antonio, recast since his 2004 turn as Ferdinand but certainly a draw in this slightly more interesting role.

It wasn’t just its proximity to my house that made the cinema experience so enjoyable – the in-house sound quality was excellent, and on the screen things was generally well presented, with a cheerful Deborah Voigt interviewing people left, right and centre. One weak link in the presentation was the film’s habit of cutting backstage immediately after the end of Acts I and II – it was a shame to break the spell in a work so deeply concerned with illusion, and a production so filled with magic.