One of the most anticipated Proms of the season was met with queues snaking down Prince Consort Road, resulting in a packed Arena – the Berliner Philharmoniker has that effect. Once the ovation which greeted Sir Simon Rattle had died down and the orchestra started playing, it was easy to hear the reason. Here is an orchestra which produces a wonderfully rich string sound, luscious woodwind solos and thrilling brass. It’s a Rolls Royce among orchestras; you detect a huge, precision-powered motor under the bonnet, but the seats have opulent padding and the finish gleams. Rattle’s choice of programme illustrated these assets in all their glory.

Can there ever have been a more appropriate final opus than Rachmaninov’s Symphonic Dances? It is a wonderful summation of his compositional career and is full of enigmatic self-quotation. The motto theme of the First Symphony, a work disastrously received after its shambolic première conducted by a drunken Glazunov, is quoted towards the end of the first dance; an affecting moment at the change of key from C minor to C major as the strings play against flutes, piccolo and chiming bells, harp and piano. The Berlin string playing was beyond full fat – it was creamily rich. Throw in the smoky alto saxophone solo and the sound almost reached a glutinous wallow.

The Dies irae chant appears, battling in the final section of the third dance with what is near enough an orchestration of the ninth movement of his choral masterpiece, the All-Night Vigil (or Vespers), underlined by Rachmaninov penning the word “Alliluya” in the score. The composer indicated, when considering allowing the Symphonic Dances to be choreographed as a ballet, that the three movements represented midday, twilight and midnight. Certainly, the crepuscular danse macabre second movement and the twelve tolling bells of the third fit this analysis, even if the titles were never published. The veiled menace of the Berlin brass at the opening of the third movement was followed by a mesmerising waltz, almost schmaltzy, almost decadent in its richness. The horns’ reprise of the Dies irae (with bells raised) was thrilling and Rattle skilfully signalled to the audience to delay its enthusiastic response, allowing the second tam-tam’s final stroke to decay naturally at the close. Yet for all these qualities, I detect that Rattle doesn’t feel entirely at home in Rachmaninov; marked tempo changes, such as the speedy accelerandos in the first movement, felt contrived. The performance was highly polished, but lacked that last degree of inky Russian gloom which pervades the work.

Any such doubts were swept away in the fabulous second half – Rattle and the Berliners gave an account of Stravinsky’s The Firebird the likes of which I have never heard before. “I think you know this already,” Rattle admitted afterwards, “but there is no audience in the world like this one.” The intensity of its listening was incredible. The most daring string pianissimos imaginable drew the entire audience in, concentrating intensely, as events in Kastchei the Immortal’s magic garden unfolded. That string sound can chill to conjure up the mysterious opening scene, or can caress in the warmth and richness of the Khorovod, which was blessed with the wonderfully rounded tone of Albrecht Mayer’s oboe solo. Trumpeters placed around the edge of the Stalls signalled the arrival of Kastchei’s ghoulish retinue, the Infernal Dance presented as a dizzying orchestral showpiece.

The Firebird is the ballet where Stravinsky shows his indebtedness to the brilliant orchestration of his teacher, Rimsky-Korsakov, and the playing here did the score complete justice. I can’t have been the only audience member running images of Mikhail Fokine’s ballet through his head, but the Berliners colourful playing brought this fantastic score vividly to life.

And the audience’s reward for such intense listening? A glorious account of the Intermezzo from Puccini’s Manon Lescaut – sumptuous strings enveloped all 6000 of us in a velvety embrace. We swooned.