Peter Maxwell Davies and John McCabe are near-contemporaries nurtured in the northwest, both students at the Royal Manchester College of Music, and this year celebrating significant birthdays. The Proms marked the former’s 75th and latter’s 70th with new concertos: the British premiere of Davies’s Violin Concerto No 2, Fiddler on the Shore, given by Daniel Hope and the Royal Philharmonic Orchestra under the composer, and the London premiere of McCabe’s Horn Concerto, Rainforest IV, by David Pyatt and the BBC National Orchestra of Wales under Jac van Steen. The Davies performance was on his actual birthday — followed by a late Prom in which the BBC Singers under David Hill gave beautiful accounts of Solstice of Light and the amazing Westerlings, inspirational Davies scores from the 1970s. McCabe is a less acclaimed figure than Davies and a more accessible one, at least if comparison is drawn with Davies’s more elevated works. They have in common a perhaps northern-flavoured belief in craftsmanship, but Davies’s is in the service of a fairly esoteric sensibility. He seeks to replace tonality with a modal method involving plainsong fragments and “magic square” permutations, and the result is a sort of warping strangeness to the sound, a sense that, though the expressive ground is interesting, it is not always firm.

McCabe has used plainsong, but if he has his arcane techniques, he keeps them quiet. His is an aesthetic of solid harmony, clear images, crisp delivery. The harmony is not unambiguously tonal, but easily graspable, and there isn’t much in his idiom that would be alien to Walton or Tippett, though he is never insistently English. His concerto’s subtitle points indeed to a modest exoticism. He is fond of evoking rainforests, and does so here with loose textures dominated by the liquid pulsings of a marimba. But the idea is to contrast this languorous world with the brisk imperatives of the city, as exemplified by jazz. Scherzo sections have a spiky syncopation that is a McCabe forte, and the first flute, Andrew Nicholson, embodied it spiritedly.

The solo part, expertly handled by Pyatt, is manifestly idiomatic and always absorbing, even though it often seems to merge with the tutti, and despite the fact that McCabe doesn’t resist stereotypical hunting rhythms. He is a serene kind of creator, perfectly happy to give us what we expect. The hand-stopped solo opening the work had something about it — a reminiscence of Britten’s Serenade for Tenor, Horn and Strings? — that suggested it would return as the close, and so it did (unstopped): an expectation crisply fulfilled and nothing if not satisfying.

Davies’s concerto was commissioned by the Leipzig Gewandhaus Orchestra, who premiered it in August with Hope, and coincidentally appeared at the Proms the night before the RPO. Riccardo Chailly conducted them in Mahler and in Mendelssohn's Piano Concerto No 1, the soloist Saleem Abboud Ashkar catching its Biedermeier brilliance to perfection. It would have been nice to hear them in their Davies piece, but the RPO was not to be found wanting. Their programme, too, began with Mendelssohn — Fingal’s Cave — as if in tribute to the Leipzig orchestra, which he for years conducted.

The programme note claimed Mendelssohn’s Violin Concerto as a decisive influence on Davies’s prolific concerto-writing since his first essay in the genre, also for violin (written for Isaac Stern and the RPO in 1985). Perhaps the new work’s continuous unfolding, the violin’s often high-lying, silvery lyricism, do indeed reflect the archetypal sway of the Mendelssohn masterpiece. Davies’s soloist does not, like Mendelssohn’s, enter almost immediately — there is a brassy preamble — but he brings a melodic line, traversing the registers, that is the material from which the structure patently grows. The folk-fiddling of Davies’s adopted Orkney home is magically transfused into the strenuous argument. The cadenza isn’t a showpiece, but a folk meditation over a double-bass pedal. As in McCabe’s concerto, the marimba comes to the fore, joined by a dancing tambourine. But the overall mood is sad and even disturbed. Hope was startlingly good. He led “Happy birthday to you” when the composer came on stage.

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