Its most famous alumnus is Amy Winehouse but the National Youth Jazz Orchestra has been a seedbed for dozens of other top musicians over the past 50 years, providing fertile ground for both Britain’s jazz scene and the pop session world. This isn’t NYJO’s first Prom – previous iterations featured in 1988, 2000 and 2012 – but it is their most demanding, and one that shows these excellent young soloists (maximum age 25) at their best.

One exceptional recent NYJO graduate is Mercury-nominated trumpeter Laura Jurd, who has written tonight’s opener, The Earth Keeps Spinning, a piece of pleasingly cyclical post-rock minimalism placed through a big-band filter. Another famed NYJO alumnus, Guy Barker, conducts an unusual version of Rhapsody in Blue. Leonard Bernstein was famously withering about Gershwin’s concerto, saying that one can omit or reorder whole sections of the piece without damaging the effect, and Ferde Grofé’s original “jazz arrangement” seems to revel in that glorious disjointedness. At times it recalls one of Carl Stalling’s jerky scores for a Bugs Bunny cartoon – a riot of hat-muted trumpets, jangling banjos and chuckling woodwind – with star pianist Benjamin Grosvenor (the one non-jazz musician here) providing rubato-heavy flourishes.

The heavy-booted big band albums of Stan Kenton remain an unfashionable cause among jazz critics, but his 1961 LP of 10 familiar songs from Bernstein’s West Side Story remains a classic. It’s a fiendishly difficult suite, which Kenton never attempted live, and lurches from spy-movie swing to fiery Afro-Cuban beats, but NYJO’s young soloists swagger expertly through its tricksy bombast. An encore of St Louis Blues sees the orchestra back on home turf, but tonight’s programme suggests that they’re even better on unfamiliar ground.

•The Proms continue until 8 September.