Most striking about the Academy of Ancient Music’s playing is its neatness: every phrase is so precisely shaped, so clean. Presumably this is down to impeccable preparation as well as an intrinsic feeling in the group for how Baroque music should sound. But their playing also sounds fresh, new, surprising. In lesser hands, their rather uniform repertoire of Handel and similar Baroque composers might get a little tedious, but the AAM find a way to bring it all to life, with the infectious, bookish enthusiasm of a favourite university lecturer.

The historical aspect of this BBC Proms Saturday Matinee concert at Cadogan Hall didn’t convince, though the high quality of performance from the orchestra with their director Richard Egarr and soprano Sophie Bevan made up for this. In theory, the concert transported us to Rome in 1707, where the 22-year-old Handel (1685–1759) had come to hear the music of the older composer Arcangelo Corelli (1653–1713). The problem was that Handel’s music was represented through a pair of cantatas – this was mainly what he wrote while in Rome, as opera was banned at the time – whereas the music of Corelli we heard was a pair of concerti grossi. With vocal music from one of these composers and instrumental music from the other, there was little sense of dialogue between them, and the programme didn’t really seem “through-composed” enough to justify its uninterrupted 90-minute duration.

Musically, however, the concert was an indulgent treat, with the Corelli and Handel pieces complemented by some roughly contemporaneous rarities: a concerto grosso for four violins by Giuseppe Valentini (1681–1753), and extracts from several sonatas for two keyboards by Bernardo Pasquini (1637–1710). As is often the case with music by less frequently performed Baroque composers, these pieces were noticeably different in style from what we think of as the norm. The Valentini piece had a beguiling simplicity to it, often pushing sequences just that little bit further than you’d expect, and creating some enchanting effects both in the expansive, elemental slow movements and the whirlwind, intense fast ones. The Pasquini extracts, meanwhile – which Egarr played with Alastair Ross – were full of harmonic surprises, and structured very freely. The two harpsichordists were both improvising their parts from figured basslines, resulting in an intricate web of chords which certainly deserved this rare concert outing.

Corelli’s pieces, their style that little bit more familiar today, were less distinctive, although spirited performances kept things lively. Lead violinist Pavlo Beznosiuk had a solo part to play in the second concerto (Op. 6 no. 12 in F major), and he shone in this role. The AAM’s dynamic shaping of their parts was particularly remarkable: they have a way of falling into sudden piano playing in a way that sounds at once surprising and entirely natural. These light-hearted numbers bookended the concert and ensured a breezy, summery feel – perfect for the balmy conditions outside.

The two Handel cantatas both offered something just a little darker: the first, Pensieri notturni di Filli (“The Nocturnal Thoughts of Phyllis”), tells the story of a love sadly discovered to be fantasy upon awakening, and the second, Tra le fiamme (“Among the flames”), tells the story of Icarus flying too close to the sun. Tra le fiamme is the larger of the two, and has the richer scoring, with a solo viola da gamba and a pair of recorders (which become oboes for the middle aria). Reiko Ichise’s gamba playing was excellent, and Sophie Bevan sang beautifully, the unusually low soprano register seemingly no challenge for her – in fact, it was the occasional higher outbursts which sounded slightly less secure. The ensemble offered an encore of “Tu del ciel” from another cantata, Il trionfo del Tempo e del Disinganno (“The Triumph of Time and Disillusionment”), whose sombre tone drew perhaps the best playing and singing of all.

This concert was presented a little like a history lesson, with informative nuggets from presenter Clemency Burton-Hill and Egarr between pieces. This is standard for a concert tackling a body of music which requires some elucidation because of how remote it is now in terms of time and fashion. But with the central programmatic idea not quite finding its feet, the high-quality performances of this Prom made for proof that this distant music, whatever its historical context, can still be made to seem alive.