Fifteen years ago I sat dutifully listening to the excellent Haringey Schools Orchestra nobly attempting to bring off the herculean musical feat of the Shostakovich Fifth Symphony. Many hours of coaching and rehearsal had clearly brought the youngsters to this point. Proud parents and friends fidgeted through the painful 55 minutes, and everyone clapped appreciatively when it ended. It was then that the delightful announcement was made that local boy Sir Simon Rattle had agreed to conduct Gershwin’s Strike Up the Band overture to round off the concert. As soon as the performance started it was as if a totally different orchestra was playing. They were in tune and in time and more to the point there was real joy in the playing. The short piece brought the house down, and by the end of that five minutes I understood exactly why great conductors are paid so much – and that Simon Rattle was indeed a great conductor.

Not that he had to do anything as miraculous to bring out the best in the Orchestra of the Age of Enlightenment at the Royal Festival Hall on Tuesday, when they performed the last three symphonies of Mozart to a full house. The OAE have certainly matured into the exponents in the UK of period instrument playing at its best. Their clean-sounding string tone is rich and vigorous, while the refinement of the woodwind and brass puts most modern instrument bands to shame. Simon Rattle, a regular guest conductor with the OAE, certainly brought an additional gravitas and vision to the concert. Light relief, maybe, after his years of politics in Germany and the burden of responsibility, steering the huge juggernaut that is the Berlin Philharmonic.

Performing the symphonies in chronological order, the grand slow introduction of the Symphony no. 39 with its military opening timpani stokes and odd harmonic twists, was sensitively done and not over-dramatised. When the light-hearted Allegro insinuated itself into our ears, is didn’t sound “light” as it can do. Flecks of anguish, emphasised in the playing, give the movement a sense of balance. In the slow movement Rattle opted for a relaxed tempo giving the opening of the movement a whimsical outdoor quality and allowed the more passionate middle section room to breathe. The Minuet third movement on the other hand was in a swift tempo giving it a Haydnesque charm. The perfectly judged Finale swept all before it and rounded off a thoroughly engaging performance, marred only by occasional over-fussy phrasing and dynamics.

Mozart’s Symphony no. 40 is surely one of the greatest minor-key symphonies in the repertoire. G minor was a key with a special significance to Mozart and it always brings out an unusually candid quality in him. With its roots in the earlier, Sturm und Drang minor-key works of Haydn, it goes well beyond them both in the complexity of its mood and in its harmonic language. The drama of the first movement was fully realised in this performance with the twists and turns of the modulations and the abrupt outbursts held together with a classical poise. Even though the music points forward to Beethoven, Schubert and Schumann, it still is very much of its time and place. The tempo of the beautiful slow movement was on the brisk side, but not rushed as has been the case in some period-instrument performances. Exquisite moments of stillness, totally unique to Mozart, were allowed to shine through. A purposeful minuet led to a dynamic finale where the virtuosity of the string writing held no fears for the OAE players. This was a near-ideal performance of a very great work.

And speaking of great symphonies, the Jupiter Symphony must qualify near top of anybody’s top ten list. Its C major grandeur is held in balance by wonderful moments of intimacy, and again Rattle and the OAE effortlessly found the pulse of the work. The opening Allegro had a steady pace and a fine pointing of the rhythms that reminded me of Beecham performances of the work. Likewise the dreamscape of the slow movement was allowed a measure of 20th-century romance which seemed entirely appropriate. The fugal finale finds Mozart taking his inspiration and technique to new heights. Of all his late music, this movement shows how he could have progressed had he lived into the 19th century. Integrating effortlessly, as it does, the Classical and Baroque styles, it also signposts the way to the riches of romantics that were to follow. Rattle and the OAE ended in the evening glorious form, clearly relishing their partnership with Mozart at his considerable best.