Nobilmente (It.). Nobly, in a noble style. As a musical term, it's almost exclusively associated with the works of Sir Edward Elgar, who first employed it in his piano transcription of the Enigma Variations. The score to his Symphony no. 1 in A flat major is headed Nobilmente e semplice, Elgar's musical equivalent of the English stiff upper lip, a restrained march initially played as but a distant memory. There was little stiff upper lip though about Daniel Barenboim's heart-on-sleeve account with the Staatskapelle Berlin, the highlight of a splendid Prom concert.

Barenboim has a long relationship with Elgar's music, but the Staatskapelle's love affair is more recent, still in the passionate, excitable phase of discovery. A couple of years ago, they made an excellent recording, but this performance surpassed even that, clocking in a little faster in an unbuttoned reading both vigorous and overtly emotional. The Staatskapelle is truly smitten with Elgar's music; most English orchestras would blush at such emotional intensity. It's entirely appropriate that a German orchestra should claim this music as their own given that it was a German – Hans Richter – who conducted the première in 1908, claiming it as “the greatest symphony of modern times”.

With eight double basses anchoring the orchestra and rich mahogany cellos, there was a purposeful tread to that opening march – an idée fixe that Elgar brings back to haunt the following movements. But the movement was soon caught up in a great sweep, led by a tremendous string attack and golden, rounded brass. Barenboim, conducting without a score, punched the air urgently, the second movement scherzo big and brash, the following Adagio lyrical, but always with a sense of flow. After its ghostly reminiscences, the finale surged and swelled, as did my tear ducts. How wonderful that a German orchestra can come to London and demonstrate how this most English music can be performed.

Elgar began his symphony in 1904, the same year that Jean Sibelius started work on his Violin Concerto. Lisa Batiashvili was the soloist here in a dark, brooding account that occasionally frowned too much. She is an energetic performer, flailing hair, dramatic back bends and knee lunges all in evidence, but she can apply ice to her fiery playing too, stretching dynamic markings to the merest whisper of a pianissimo – a daring thing in the RAH's unforgiving acoustic. Barenboim, sometimes conducting with little more than a shrug and a poke, was content to play a supporting role. Batiashvili phrased tenderly in the Adagio di molto, but in the finale, with snarling horns and hard sticks rattling on the timpani, there was little sense of dancing joy in what Donald Tovey dubbed a “polonaise for polar bears”.

Barenboim is always afforded a hero's welcome in London and the ecstatic audience response was rewarded with encores featuring each of the evening's composers: a yearning Valse triste and a brusque, bustling Pomp and Circumstance March no. 1 all the better for not entertaining the jingoistic lyrics usually associated with it at this address. Someone put Barenboim in charge of the Last Night.