Beyond the unprecedented qualities of Bach's Brandenburg Concertos, there is a kind of timeless alchemy at work within all of them which seems to transcend the normal considerations of instruments and interpretation. Died-in-the-wool purist, 'modern' instrument devotee or middle-of-the-road music-lover: it makes no difference to the viscerally transporting effect this music conjures.

That being said, a performance by the Orchestra of the Age of Enlightenment – a band whose very identity has been tied up with the Brandenburgs since a landmark recording 25 years ago – is a prospect of particular delight, and the opportunity of hearing them play the set in its entirety last Thursday at The Bridgewater Hall was certainly one to be seized.

Thirty-one years in the field, the OAE continues to prize its community ethos and well-honed agenda to bring period instruments into the mainstream: a message it delivers extremely well, both through a public persona of heart-on-sleeve chutzpah, and by its highly expressive physicality in performance, although this is one of virtuosity and energy, not mere flamboyant display. Violinist and director Huw Daniel may have virtually bobbed and danced his way through the concert, but his near flawless playing navigated the multitudinous tasks with exceptional finesse. He was sinewy and nuanced in the slow movements, ebullient and effervescent in the fast, his ornamentation fulsome and inventive without ever stealing from the momentum of the phrase.

Daniel's ensemble work betrayed an empathetic sensibility too, as in the concertino dialogue with flute (the remarkably expressive Lisa Beznosiuk) in the Affettuoso of Concerto no. 5, which found just the right level of whimsy. If harpsichordist Steven Devine's exaggerated arpeggiation over-egged the sentiment here, there were no such liberties in the first movement: a no-nonsense Devine brought the harpsichord glitteringly to life, in both the cadenza (a reminder of Bach's own immense prowess as an improviser) and in the rippling and swirling flourishes of the concertino passage-work.

There were myriad examples of how the tonal purity and balance of the one-to-a-part ensemble was able to expose – reveal even – details of the score which can often, with larger instrumental forces, be just too subtle. So too were certain players able to illuminate themselves alongside the spotlighted soloists. Cellist Luise Buchberger's poignant delineation of the sequential figurations in the continuo of the Fifth's first movement not only swung the listener's focus away from the harpsichord, violin and flute, but more memorably, shone a shaft of radiant light on one of the most beautiful bass lines in all of the concertos: a truly transformative moment.

Other featured players were also exemplary: recorder players Rebecca Miles and Ian Wilson in the Fourth, and in the Second, trumpeter David Blackadder and oboist Katharina Spreckelsen, whose gorgeously honeyed tone seemed particularly favoured by the warmly reverberant acoustic of the hall.

If there was one concerto which lacked that sense of conviviality so tangibly conveyed in all the others, it was the Sixth. The only concerto without violins, Huw Daniel may have been enjoying a well-earned break, but the cohesion and discipline of his playing was missed, and viola players Simone Jandl and Max Mandel seemed uneasy in their leadership. A tentative and uneven first Allegro never quite settled, whilst the second Allegro knitted together only progressively, the continuo doing its best to galvanise the pulse.

Though the question of tempo is possibly less subjective with Bach than any other composer, it may be worth raising it here, only insofar as those few occasions where choice of tempo seemed driven by a need to dazzle at the expense of the 'dance'. In the First's opening Allegro, an overly brisk pace precluded the declamatory yet bustling, four-in-a-bar swing, and somewhat compromised the horns' articulation of the cross-rhythms of their 'hunting calls'. And in the first movement of the Sixth, the nervy and restless feel undermined the 'funkiness' inherent in the swaying rhythm and dark lumbering of the gambas and violone. While the scamper of the Third's opening Allegro paid off, the race to achieve one-in-a-bar verve in the second didn't, and instead took the edge off the upper strings' intonation. Elsewhere, tempos hit the spot, facilitating both rhythmic buoyancy and virtuosity. Minor quibbles did little to dampen a re-invigorated – enlightened even – admiration of both the music and its musicians.