Karol Szymanowski's Violin Concerto no. 1 defies conventional structural analysis: from its quirky opening of woodwind chirps over ostinato strings to its delicate, evanescent ending – followed by the shortest of little musical jokes – it's music that goes in all manner of directions, seemingly at the composer's whim. Yet there is magic at work: as you wander around this diverse musical landscape – sometimes briskly, more often meandering – you never feel in anything other than safe hands.

Especially, that is, if the hands are those of Nicola Benedetti, whose career took off as a result of a competition performance of this concerto, has recorded it and has performed it countless times since. What distinguished last night's performance was the utter purity of tone of her high notes and the scales and ornaments around them, starting from her very first notes rising from nothing over a background of harp and strings. It's not just that she is playing an intrinsically great-sounding Stradivarius, it's also that the timing and dynamic contour of every phrase is created with utter confidence. Even within a single held long note, her ability to give shape and progression to the sound was wonderful.

Our other guide on this occasion, conductor Krzysztof Urbanski, turned out to be equally reliable. When he's not making musical jokes, Szymanowski's music can get truly rhapsodic: there are passages of great sensuality, some of the composer's unique ability to create a wave of sound that breaks over you, and some imposing orchestral climaxes. Urbanski is very young (and looks even younger), but conducts with extreme precision, and the London Symphony Orchestra seemed to respond accurately to every nuance from his baton.

Brahms' Concerto has been described as a "concerto for Violin against orchestra": Szymanowski's is very much the opposite. Benedetti plays it that way, without excessive mannerisms, vibrato or attempt to grab the limelight – in fact, the one weakness of the performance was that lower register, heavily accented passages could have done with a bit more bite – she simply allows one to drink in the lyrical beauty of the music. Her encore was in similar vein: after a touching dedication, she was joined by three members of the LSO in a delicate rendering of the slow movement from Tartini's Concerto in A major.

The other pieces on the programme were both Russian and both very popular pieces. The curtain raiser was the overture to Glinka's Ruslan and Lyudmila. It's a rowdy, upbeat number by nature, and Urbanski took it at blistering pace, showing off quite how slick the LSO strings can be. I found myself glad that unlike opera singers, violinists don't need to breathe.

The second half of the concert consisted of Ravel's arrangement of Mussorgsky's Pictures at an Exhibition. Both Mussorgsky's original and Ravel's orchestration are works of genius – the original for its abundance of imagination and texture and the way it allows the listener to paint mental pictures of their own, and Ravel's work for the sheer brilliance of its orchestral colouring. It's a work that's been a favourite since childhood and one of which I know every note, which always gives the worry that the performance may not live up to expectations. What happened was the exact opposite: Urbanski and the LSO were outstanding, making me fall in love with the work all over again.

When orchestral colours are so vivid, it takes a great deal of individual virtuosity and precision of ensemble timing to make them really shine at their brightest, and that's exactly what the LSO gave. I lost count of the number of times where I felt that a phrase had really excited me, played just the way it should have been. Within the darkness of “Gnomus”, a hundred orchestral details came through clearly, especially cello phrases, the shimmer of cymbals and telling interventions from percussion of all sorts. The second promenade rang clarion clear from horn and trombones. The saxophone solo in “Il vecchio castello” slid sinuously around its dark background of bassoon and strings. But it was at “Bydło” that the performance really took off, with the tuba solo fabulously played and the following crescendo from the double basses leading the orchestra into a stunning crescendo and diminuendo – in fact, the double bassists, all nine of them seemed to be enjoying themselves hugely.

I won’t list every picture, but Urbanski continued to infuse each moment of the music with life and interest, until the joyous climax of “The Great Gate of Kiev”, where he showed true feel for the music's dramatic sweep.

This was a concert which included both familiar and less played works, and in both, it showed the LSO absolutely on the top of their game. At 33, Urbanski is amongst the youngest cohort of top conductors and the prospect of seeing a lot more of him is exciting.