Deutsche Kammerphilharmonie Bremen, Barbican Hall, London

As fashions come and go, the music of Felix Mendelssohn stays well out. Popular, yes, but not serious is his image in Britain, forever tainted by the mountains of Victoriana that others composed under his spell. In Germany at least, there's an element of atoning for past anti-Semitism – his music suffered a Nazi ban – but what about listening to him on his own terms? That was the aim of Sunday's efforts by a young German orchestra and its British conductor, Daniel Harding, backed up by essays on his central role in 19th-century intellectual and artistic life, and rewarded by a large and attentive audience.

The Deutsche Kammerphilharmonie Bremen is a chamber-sized group rather than a period-instrument one. It has taken on a few techniques (and a pair of trumpets) from the period movement, but its freshness and virtuosity are more a matter of attitude. Its musicians play chamber music, as in an afternoon concert of Mendelssohn's Octet and a wind-ensemble arrangement of his Midsummer Night's Dream. And the habit of listening closely and responding with immediacy shows up the moment the full orchestra plays.

For the evening concert, the programme was standard, but given with energy, fire and commitment. The Hebrides Overture was a game of two halves, first quick and breathless, then opening up with three big surprises, two of them spacious – especially the return of the main melody on clarinets – and then an extra burst of speed with no let-up, when the sudden quiet ending seemed to shock listeners who must have thought they knew the music backwards.

This performance wasn't quite all of a piece. The Scottish Symphony very much was, taking the generosity of phrasing to logical conclusions and freeing up the tempo structure, especially in the ebb and flow of the opening movement, which moved with complete cohesion between soulful languor, fiery energy and unworldly stillness. Unlike Schumann, whose music the orchestra played with flair at the Proms 18 months ago, Mendelssohn doesn't gain from having smaller string sections: the woodwind are deployed brilliantly to start with. What you do get is rhythmic definition at speeds that big orchestras can't do, and this made edge-of-seat listening out of the interplay between wind and strings.

So: phrase this melody-based music with passion, even sensuality, pace it with wit, and it starts bursting out of its skin like an unknowing precursor of Tchaikovsky. Those symphonic forms aren't as conventional as they seem to a lazy ear. Mendelssohn's First Piano Concerto is more obviously big on formal originality, as it telescopes everything into what, this time, was 15 minutes of perfection. Nikolai Demidenko was at one with Harding and the orchestra in weighting the eloquent lines with exactness, and kept up the sparkle and dash as he made the fast music fly. Heady stuff – and to think generations have been brought up to think of it as sugary and superficial.

One final surprise: the encore was by Beethoven. Let's hope this equally fizzy performance of the Prometheus Overture was just done for fun, rather than to show where Mendelssohn cribbed his symphony's opening theme from. Or maybe it was flying a kite for some future project – an all-Beethoven return visit ought to be just as revealing.