Thomas Adès' music has a rawness that only comes across heard live. This seems particularly true when he conducts it himself. Gone are the smooth contours of recordings and other conductors, replaced by a focus on infectious rhythm and sometimes brutal colours. His lyrical tendencies therefore become all the more powerful.

Tevot is the perfect example. Composed in 2005-6, the title evokes an image of being carried through chaos in a safe haven. The Hebrew word tevot is a term for musical barlines: in its singular tevah, it means both the ark built for Noah and the basket made for Moses by his mother to drift him down the Nile. Bars carry music to its conclusion, whilst the ark in Tevot symbolises the earth helping us through space. Tevot thus plays on Adès' earlier Asyla and extends it.

Adès' brilliantly original style seems, like that of all excellent composers, to pick up on myriad influences and more than reimagine them in new contexts. In Tevot, for instance, there are piccolo and flute lines at the start of the adagio second half which evoke the finale of Mahler's Tenth Symphony, string passages of surging power that bring the end of Tchaikovsky's Sixth flickering into mind, and more than a hint of the terrors of Shostakovich's Fifth in some of its phrasing. This, of course, is in addition to the much more modern traits, like the dancey rhythms either bubbling below the surface or thrashed out on percussion, or the jazzy sense of improvisation, or the Ligeti-like use of harmonics and atomisation of the orchestra. But Adès' music is so fearsomely original, so immediate and affecting, that it feels wrong to write in such a way, rather than accepting it as something at once startlingly new and firmly rooted in the past.

The piece starts with Adès' characteristic string figures, brassy chords interjecting as they do in In Seven Days' sections referring to the stars, moon, and sun. We are clearly in space, glistening textures evoking emptiness and far-off promise. So it continues, high strings playing on the bridge and winds as if on a precipice. A scene where thwacking percussion becomes too much to bear forces the music to collapse into Adès' spectral lyricism. His harmonies are never clear, always elided into and usually alien, but they are often in his tendermost moments oddly comforting. Climaxes swell past, building all the time, giving a sense of being slowly carried aloft. It ends, finally, with major-key glory. Here, the colours created by the LSO were testament both to Adès the conductor and Adès the composer. So too was an emotional range approaching that of Mahler. Tevot achieves a sense of transcendent journey that, wedded to a compositional voice devoid of cliché, deserves such comparisons.

Adès' concertante work for piano, In Seven Days, is marginally less successful. Originally written as a 'video-ballet' accompanied by images created by Adès' partner Tal Rosner, something intangible is missing when performed as pure music. Partly this is because the role of the piano is never clear, not that it need necessarily be. Its programme – the seven days of Creation – allows Adès' talent for colour to emerge, from the juxtapositions of light and dark to the image of slow-growing piano-plants embedded in the lush harmonies of soily strings. Again Adès' control of structure is unflappable, and the technical quality of the writing – particularly in the fugal sections that open the piece and describe the creation of animal life – is startling. In Seven Days has its emotionally-powerful moments too, like the earlier Tevot. As the energy of creation slips away, the piano alone slips downwards as if in a bluesy reflection on a long night in a bar, slowly down to darkness and sleep. And as the seventh day passes, the contented stillness of a divine smile seems poised to give up on rest and start creating once more. There could be no better advocate for this work than Nicolas Hodges, whose dexterity allows fervid vitality to sit easily with reflective placidity. The LSO played with the confidence they bring to the classics: these were outstanding performances.

The première of Hidd'n Blue, by Adès' only student Francisco Coll, was an apt overture to the concerto. Its scary view of a polarised world of extremes seemed full of Adès-like gestures refracted through an extended scream, leaving only a lone violin wailing. Coll is clearly one to watch.

Five of Mahler's Wunderhorn settings prefaced Tevot and, 'Urlicht' aside, tenor Toby Spence struggled to be heard against a sparkling LSO. Adès conducts Mahler, on this evidence, like he composes, revelling in extremes. Spence was excellent in the pained, resigned duty of 'Revelge', but the primeval legato needed in 'Urlicht' was absent. Some of the music seemed to sit too low for Spence's voice, particularly in 'Der Schildwache Nachtlied' and 'Wer hat dies Liedlein erdacht'. Still, the songs were delivered with his usual vigour.