Sitting in the kitchen of his charming home on the leafy fringes of Morningside, with its cool nordic decor, Haflidi Hallgrimsson seems comfortably distanced from the financial disasters and volcanic eruptions that wrought havoc on the small population of his native Iceland.

Ever since he was invited, nearly 40 years ago, to join the newly formed Scottish Chamber Orchestra as principal cellist, Edinburgh is where he has lived happily with his piano teacher wife Heida, raising their three sons, Almar, Andri and Stefan, in preparation for careers in widely separated parts of the world.

But in fact, on the morning we have arranged to talk, things are less calm than they appear. Though coffee is ready in the cafetiere, there are packing cases on the floor, empty shelves on the walls and suitcases at the front door. Haflidi, in his 70th year, and Heida are about to move. A new chapter in his life as a major Icelandic composer, and in hers at the keyboard, is beginning – though not in Edinburgh, and not in Iceland either.

Soon after our meeting they are en route for Bath, where they have bought a Georgian cottage comfortingly like the house they are vacating, with space for a studio in the garden where Hallgrimsson will continue composing – and painting, because, like Mendelssohn and Schoenberg before him, he finds art almost as inspirational as music, the one, indeed, being a huge influence on the other. There is also, he says, the prospect of better weather. But why, in the first place, did a successful orchestral cellist ever want to give up the most lucrative portion of his career in order to concentrate on the uncertainties of composition?

Hallgrimsson’s flair for his instrument first showed itself at the age of 10 in his hometown of Akureyri on the north coast of Iceland. Lessons followed in Reykjavik and later at the Santa Cecilia Academy in Rome, where it was clear he was going to become a sought-after player. After studies with Derek Simpson at the Royal Academy of Music in London he won the Madame Suggia Prize in 1966, befriended the violinist John Tunnell and began to “win assignments on and off”. It was an established way into music, and he was ready for it.

When Tunnell, pillar of the Vesuvius Ensemble, moved north to lead Scotland’s first full-time chamber orchestra in 1974, Hallgrimsson soon followed. It was an exhilarating time. Scottish Opera, against all the odds, had established itself as an exemplary British company with a Scot, Alexander Gibson, at the helm. The RSNO was flourishing. The Queen’s Hall was becoming Edinburgh’s place for chamber music, and Hallgrimsson was the first of a succession of fine new cellists to make his mark.

Before he left London, however, he had been studying composition with the quirky Alan Bush, whose political incorrectness, growing more contrarian with every word he uttered, proved a considerable stimulus. Meeting him for the first time in his rooftop hideaway, Hallgrimsson was handed a two-bar fragment of music and told to turn it into a 20-minute string trio. After closely inspecting the result, Bush looked at Hallgrimsson and said: “You are a composer.”

But Hallgrimsson’s time had yet to come. As an early member of the SCO he faced the endurance test of playing in the pit for Scottish Opera as often as for symphony concerts. “I still needed to know,” he says, “if there was any music in me. So I tried to combine composing with playing, but it didn’t work.”

In the end, composing won. “Let your ears be your guide,” Bush had said to him, but his eyes also played their part. As early as 1969 he had performed one of his first compositions – Solitaire for solo cello – surrounded by an exhibition of his own drawings and paintings. It was a turning point, though it was some years yet before he was commissioned by the SCO to compose his Still Life, a musical response to a painting by the Edinburgh artist Craigie Aitchison, whose tiny picture of the crucifixion was still hanging in the hall on the day of my visit.

With his wife’s support, Hallgrimsson started composing full-time. Immaculate manuscripts, models of nordic design with a bias towards music for a solo string player and orchestra, began to accumulate. Today there are more than 100 of them, among which his Cello Concerto for the great Norwegian soloist Truls Mork, jointly commissioned by three orchestras in 2003, remains a landmark.

Back in his homeland, where “to avoid restlessness” he says he goes twice a year, he recently became composer-in-residence with the Iceland Symphony Orchestra, whose latest conductor is Ilan Volkov. Commissions (one of them a Concerto for Orchestra) are ongoing and a recording of his Symphony No 1 was promised.

Undamaged by Iceland’s bankruptcy, the arts are thriving in Reykjavik, where the striking new Harpa Hall, which opened in May, has a volcanically red auditorium seating 1500 people and a smaller one in cooler blue-green. The long-established Nordic Music Days, a lavishly moveable feast, erupted there this year with Martyn Brabbins as one of the conductors of its tally of 50 new works, and with Caput, Iceland’s equivalent of the Hebrides Ensemble, among the performers.

Meanwhile, here in Scotland, the world premiere of Hallgrimsson’s Violin Concerto – another Icelandic commission – is approaching in December, with Jennifer Pike, a gifted young BBC Musician of the Year, as soloist, and with Enrique Mazzola conducting the SCO. The manuscript, spread out in Hallgrimsson’s kitchen, the notes sprouting from a characteristically slow, stealthy opening section, looked as lucid and as beautifully designed as any of its predecessors (although none of his sons has followed in his footsteps as a composer, one of them is an architect in Brussels). After the SCO performance, this circling music, as Hallgrimsson calls it, will pursue its own nordic trajectory, with performances in Iceland and, let us hope, other places, too.

Haflidi Hallgrimsson’s Violin Concerto will be performed at the Queen’s Hall, Edinburgh, on December 8 and the City Hall, Glasgow, on December 9.