It was an uninspiring drizzly Sunday morning by the Sussex seaside. Those seeking inspiration could find it in the form of the Elias String Quartet, playing to a healthily-sized late morning audience at Brighton's Corn Exchange. The Elias are an accomplished and versatile ensemble; both these qualities were in evidence today. It may have been a "coffee concert" but this was as full and varied a programme as you'd find in the traditional evening slot, with characteristically first class renditions Haydn and Mendelssohn. However, Britten's first numbered string quartet sat uncomfortably in the middle.

The Elias made the most of the venue by playing in the round, an arrangement which created an intimate feel despite the hall's largesse. The Grade I-listed venue itself is overdue more than a lick of paint – and some better soundproofing – but we were assured that money for a renovation project is now secured.

Haydn's Quartet in C major Op.54 is relatively short but beautifully formed, the second quartet written for Hungarian violinist Johann Tost. Unsurprisingly given this dedication, it feels like the Violin I show for several of the movements. An extraordinary Adagio involves a stream of conscious-like first violin part meandering romantically over the other strings, mournful accidentals providing a subtle hint of Hungarian folk. Departing from vibrato here added extra rawness to the emotion, while Sarah Bitlloch hit just the right tone in the violin's wanderings. Bittloch's lead was strong overall, also working seamlessly with second violin Donald Grant in passages of interplay between the two.

Haydn's wit is often remarked upon. Here, that wit came across memorably. The comic timing in the opening Vivace was well-judged, the opening theme refusing to end without an two extra notes. These cheeky notes ascend before disappearing into a carefully placed pause, expecting an answer. Elias are a group so comfortable and experienced together that the timing of these pauses felt easy as pie. Their excellent balance and rich tone were a constant right down to the Finale which, after several changes of direction, settled down to a contented end. If there's any criticism to be made, it was that the sudden move into rhythmic energy in the Menuetto felt a little heavy handed, especially after the exquisite Adagio. As an opening work though, this quartet was spot on; neat in its length, inventive in structure and humour, it was the highlight.

Moving on to Britten's String Quartet no. 1 in D major was a difficult corner to turn. The Elias quartet did not seem at home to begin with. The Andante sostenuto employs close dissonance to create tension. Upon first rendition, the held chords under the careful cello pizzicato seemed to lack sustenance and clarity, but it grew more convincing when the motif recurred, drawing in the ear. Quirks of a seaside venue provided a strange fifth instrument in the form of a flock of seagulls. They arrived outside the window with noisy screeches just when the music had sunk to a ponderous quiet. I found this to be timely, creating a mental picture of a bleak seascape.

This quartet foreshadowed Peter Grimes and those uneasy atmospheres and harmonies were well crafted by the Elias. As the work progressed, moods shifted and grew beguilingly, but placing it after Haydn made it feel lacking in shape. Still, stirring emotional peaks once again showed the power of the Elias' combined forces. Their tight sound and easy blend were most compelling in the sparky passages of the Allegro vivo and energetic interruptions in the final two movements.

Mendelssohn's String Quartet no. 2 in A minor was a return to a comfort zone. The work was composed as a musical love letter to Beethoven, who had recently died. With the Elias having performed all the quartets during their "Beethoven Project", their enjoyment of its style was evident. Demonstrating the 18-year-old Mendelssohn's gift for spinning melody, it's a delightful journey. There was ample bite and energy in some sections and pure Romanticism in others; an easy journey to go along with. A playful tune in the Intermezzo stood out, and a wide range of articulation kept things interesting. There was a clear sense of coming to an end as the initial Adagio made its reappearance in the final Adagio non lento, but not before a wonderful solo violin ad libitum interlude. With its hint of Beethoven's Ninth Symphony, it is perhaps Mendelssohn's tender voice of mourning for his fellow composer.

A charming arrangement of a Scottish tune made a gleefully incongruous encore, bringing back the smiles which Hayden's comic sense had first drawn. This concert showed the Elias' ability to imbue their performance with equal energy and sensitivity, particularly in their understanding of Haydn and Mendelssohn. They are a class act.