When should a conductor turn round? Excepting choir stalls, it feels very unusual for a director to face the audience head-on. The conductor's back forms the final barrier between audience and orchestra, the marker that there is a performance underway. Only by lowering their hands and turning round does the conductor break down this wall and allow the audience to acknowledge the orchestra through its applause.

Bringing this convention into sharp relief on Wednesday night was the Britten Sinfonia, with conductor and soloist Barbara Hannigan on the London leg of their UK tour. Far from Hannigan's core repertoire – the daunting peaks of 20th- 21st-century Modernism – we heard music Classical and Neoclassical, a reflection on the enduring influence of Classicism in a programme of the soprano's own invention. Each half began with a Mozart overture, followed it up with a showcase scena, and finished with a purely instrumental work. The result was a totally convincing demonstration of the Canadian's musicality, adaptability, and flair.

What struck me first of all, though, was the sheer force and power of the Britten Sinfonia's strings. Led by Jacqueline Shave, this is a section with real bite, and stringent articulation very much redolent of a period ensemble. In the sprightly overtures, none of the otherwordly, butter-wouldn't-melt grace characteristic of much modern Mozart performance; instead, a vital, primary-colour rush of textures and moods, with woodwind highlights brought out effortlessly. Idomeneo was big and bold, La clemenza energetic and thrilling. Hannigan's conducting is remarkably economical, but these tiny, precise motions get big results from an alert band, and I heard nary an ensemble slip all night.

Just so in Haydn's Symphony no. 49 in F minor “La Passione”, where the opening's contrasts of light and dark were very finely graded; the major passages gave real consolation, and though slightly metronomical, the sense of flow and discourse (so important for Haydn) was impeccable. My doubts about Hannigan's aversion to rubato were compounded somewhat by a staid – even dour – minuet, but the energy of the frantic second and fourth movements was irresistible. Tuttis had a staggering weight and force, but diminuendos happened on a knife-edge, and those strings again; the tremolos in the finale were absolutely furious, a terrifying evocation of passionate grief driving us towards the angst-ridden conclusion.

It was a detail-first approach with many positives, but I felt the wash of micromanagement occasionally sacrificed a more 'macro' view, and the longer lines felt somewhat lacking. Of course, in Stravinsky's Pulcinella Suite, details are the name of the game. The orchestral suite from the Baroque-inspired ballet is a feast for orchestras, replete with harrowingly virtuosic writing, scrumptious 'wrong-note' harmony, and an indefatigable charm. Genteel good humour certainly informed the bulk of Hannigan's interpretation here, a contrast to the powerful, almost aggressive positivity of what we had heard before.

If it occasionally felt a little stale, this was only because of a hands-off approach that mostly paid healthy dividends. Hannigan largely left the players to their own devices, and the quality of the wind playing in particular was exemplary. Etienne Cutajar handled the outrageous demands of the principal horn part with ease and panache, while Paul Archibald's high trumpet playing in the finale gave the music a powerful shot in the arm, bringing the concert to a thrilling conclusion.

Let's not forget who the star was here, though: Barbara Hannigan. Her two solo spots were a revelation, as much for stagecraft as for the sheer quality of her performances. Going into the dark opening of Anne Trulove's scene from The Rake's Progress, the soprano began conducting the orchestral introduction, but to deliver the lines “No word from Tom” she turned, slowly, to the audience, her face a mask of confusion, sorrow, and loss. It was a startling cognitive shift that brought us wholly into Auden and Stravinsky's troubled world. All the way to the blazing C major cabaletta that closes the scene, Hannigan was wholly convincing, and that final top C was a thing of beauty.

Hannigan's phenomenal technique is perhaps her defining feature as a singer, and nowhere is this better shown off than in Mozart's Bella mia fiamma, addio! which, according to the likely apocryphal story, was written to challenge a soprano who demanded a concert aria from Mozart. If she could make it through the chromatic thickets, laden with hair-raising leaps, unscathed on the first reading, she could take it to the public. Fortunately for us, she did, and Hannigan has made a career out of making such acrobatics sound easy. This was a virtuoso performance in every respect, and one that was a real pleasure to witness.