There was a buzz about St Ives. Attracted by St Ives Bay's buttery natural light, dramatic landscape and affordable accommodation, artists flocked to the seaside village in the years after each World War. Artists were spending time with their peers, in social settings and in each other's studios. Conceptual ideas about what art could mean were moving from café and pub debates to reality.

Formed in 1927 and based in St Ives' Mariners' Church, the St Ives Society of Artists was a group of traditionalist painters. Led by maritime artist George Bradshaw, by the end of the Second World War, the Society was doing its best to assimilate the influx of newly arriving, exciting young artists who had elected to make the Cornish fishing town their home.

Born in St Ives in 1918, Peter Lanyon was already in place. His friends Barbara Hepworth and her partner Ben Nicholson had upped sticks from London and arrived in the town as the war broke out; the likes of Naum Gabo, Terry Frost and Patrick Heron followed.

The St Ives Society of Artists' assimilation attempts had included granting the incoming wave of artists wall space in their group exhibitions held in the seaside town's Mariners' Church. However, by 1940 more and more of the new artists' work was being relegated to the gloom of the church's crypt.

Then – as if this relegation was not making things clear enough – illustrator, Society fellow and friend of Bradshaw, Harry Rountree, declared the younger artists should stop making what he called 'French rot' – a reference to the influence of French Modernist aesthetics.

If anything, Rountree's grumpy comment spurred them on. In 1947, Nicholson and Hepworth – now joined by Wilhelmina Barns-Graham, Bryan Wynter, Alice Moore, Misomé Peile and others – formed a splinter collective. Taking their name from their place in the church's gloomy recesses, the Crypt Group may only have existed in name for a couple of years (key members went on to form the Penwith Society of Arts in 1949), but their conscious move from the old to the new underlined how St Ives was now a host to an informal Modernist art school.

Egging each other on, artists who had been using drawing to sketch out ideas for landscape paintings and portraits now used the medium to give their percolating concepts wings. They rummaged through a grab-bag of prevailing European influences, from the Dadaist movement to Cubism and the dawn of abstraction, their drawings functioning as developmental documents.

Scottish mathematical biologist D'Arcy Wentworth Thompson was also a somewhat unlikely source of inspiration. First published in 1917 and then reissued as a longer version in 1942, copies of his book On Growth and Form were being passed around among the artists.

Energised by how the book – and its illustrations – pointed out the similarities between mathematical geometry and the shapes that occur organically in nature, the St Ives Modernists folded Thompson's findings in with ideas being explored by European movements and set about bringing contemporary, radical art into play in Britain.

The difference between Wilhelmina Barns-Graham's Cornish Landscape drawing from 1940 and works like St Ives from 1947, is a marked example of how artwork made in St Ives at the time narrated this fresh direction of travel.

The first image is a relatively faithful recreation of a landscape. The subject matter's perspective is intact, some elements are clearly far away and others are nearer. Yet within the drawing, Barns-Graham has been intrigued by the meandering, winding hedges between the fields. The hedges are inked in as thick, bold lines that do not necessarily taper off as they move toward the horizon.

By 1947, however, while Barns-Graham still cares about perspective, her drawings are made to convey the ambiguity of time, rather than how objects relate to each other. Her meandering lines remain but they are more gestural and impressionistic.

For the St Ives drawing, Barns-Graham creates more ambiguity. The dowdy tonal washes over drawn lines invoke an hour that could be the moments just before a storm or just after. Barns-Graham's lines are little more than scratches here. They hint at the shapes of buildings before colliding into abstraction. This was the Modernist way: use experimentation to communicate emotional subjectivity while moving forward, away from traditional modes of artistic representation.

Similarly, Barbara Hepworth's drawings illustrate the progression of her artwork during the first part of her St Ives life. Two Nudes Standing from 1947 is a pensive drawing of a female figure.

Shading is provided by way of smudges and cross-hatching. There are the beginnings of an interest in the lines around the figure's profile, hair and hands and her self-portrait from three years later shows signs of refinement, largely in the more confidently drawn lines.

By 1957, though, Hepworth's focus had shifted fundamentally. Group – Stone could be by a different artist altogether. All that remains from the previous works are the lines, rendered here in speedy scrapes of ink.

Ripped from a sketchbook, Winged Figure (for Brass) is clearly a study for something three-dimensional.

Everything and anything conventional in terms of tradition is gone. Instead, Hepworth has attacked the paper with what could even be a felt marker pen, and the resultant drawing is an exhilarating depiction of freedom in motion.

As Hepworth drifted further into her sculptural work, Ben Nicholson remained faithful to exploring how paper, board and canvas could contain his explorations. While his predecessors had painted the tones and shapes of landscapes with a certain objectivity, Nicholson painted what it was like to be inside the landscape: the sensations felt by being assaulted by nature's magical curves, colours and angles.

Created using pencil and charcoal and by scratching into oil paint, 1946 (window in Cornwall) offers blocks and lumps of understated tones.

It is a scruffy, unfinished drawing in the way that nature itself is often scruffy and never finished. Picasso, Mondrian and other European artists had been throwing artistic conventions out of the window for a few years already, and Nicholson's shift in style was just as progressive.

Elsewhere, in the hands of a more conventional artist, a view of St Ives might be affectionate and orthodox. Not Nicholson. His December 1951 (St Ives oval and steeple) shows an ellipse tangled in with pencil strokes that eventually stretch out to describe a townscape. Presumably this is the kind of 'French rot' Rountree found so objectionable.

The still life drawing's origins are traceable to biologist D'Arcy Wentworth Thompson's venerated On Growth and Form book. As part of his studies, Thompson discussed the prevalence of oval shapes in nature, from animal, bird and insect eggs to the shape of a sea sponge's cells and human blood corpuscles.

Nicholson's egg-shaped form dominates the December 1951 (St Ives oval and steeple) drawing and is even more obvious in sculptural works made by Barbara Hepworth and Naum Gabo.

Model for the Esso Project, Radio City, New York

Gabo's Model for the Esso Project sculpture maquette from 1949 is contained within an oval, and there are numerous examples in Hepworth's pieces, including Pelagos, created the same year.

Portraitist Leonard Fuller had arrived in St Ives in 1938 to form the St Ives School of Painting with painter Borlase Smart. Fuller was known for his teaching skills, something that drove artist Terry Frost to relocate to St Ives in 1946. Fuller's mark-making process was more formal than the groundbreaking methodologies developing in the town but he understood that art needed to evolve, and the St Ives School of Painting gave artists the chance to work in an organised environment.

Frost began to develop his Modernist technique under Fuller's tutelage, pushing himself on from earlier, more traditional ways of working, seen in pieces like his 1944 portrait of Sergeant Ernest Little.

Sergeant Ernest (‘Ernie’) Little, 5 Buffs, as a Prisoner of War in Germany or Poland

Made between 1948 and 1949, ink skitters across the page for Frost's Fishing Boat drawing, giving the impression of a careworn vessel that had been knocked about by a life at sea.

Frost would go on to become studio assistant to Barbara Hepworth.

By the mid-1950s, the influence of the new Abstract Expressionist movement was making its way across from America to the UK. The freedom in art created by Jackson Pollock, Mark Rothko and more overlapped with the ambitions of the St Ives artist residents as their work further embraced abstraction.

The age of Modernism may have drawn to a close, but the town of St Ives – as a platform for the exchange of ideas, as a place of topographical inspiration; even as a site for dismantling established aesthetic themes and rebuilding them as modern art – had left an indelible impression on British art history.

Simon Coates, writer

This content was funded by the Bridget Riley Art Foundation