Kindred spirits in the frame

One learns all the time.

I'd always had Ben Nicholson figured as a Modernist in the image of Picasso (see the latest show at the Tate) with a passionate affair followed by marriage (his second) to the sculptor Barabara Hepworth, an artist who had retreated to St Ives in the war, where he remained, returning to figuration in his later art.

What I hadn't taken on board was his close friendship with Piet Mondrian through the Thirties and that he had brought over the great Dutch abstract artist to London as war broke out in 1939 and that the two had stayed painting side by side in Belsize Park until the bombs had forced Nicholson to Cornwall and Mondrian to New York .

Enlightenment has come in the form of a brilliant small show at the Courtauld, Mondrian//Nicholson: In Parallel, in which the relationship is recounted through 18 works, all of them masterly, from the moment when Nicholson visited Mondrian's studio in early 1934 to the time when the two went their separate geographical ways some seven years later.

The curators are at pains to explain that this is a study of parallel lines not a revelation of convergence. Both men were independent spirits as far as their art was concerned and both were well set on their own abstract courses when they met. The exhibition starts with two works from just before their first meeting. In 1933 (Six Circles), Nicholson is already embarked, rather roughly, on his excursion into squares and circles incised into wood, introducing shadow and the handmade into the purely geometric. Mondrian meanwhile is already far down the road with Composition with Double Line and Yellow, in his single-minded pursuit of "classic" squares of colour and line held in dynamic but still juxtaposition.

There is no doubting their differences. Stand back in the main gallery where their work is shown side by side and there is no doubting whose is whose, for all the similarity in geometric abstraction. Nicholson, even in his most Mondrian-like pursuit of the tension between shape and line, has colour at the centre of the picture, the fulcrum around which the squares and circles expand. Mondrian more and more pushes colour to the extremities of the picture, holding the composition in the dynamic of his lines and rectangles. Nicholson uses muted to Mondrian's absolute insistence on primary colours. Mondrian builds up his whites, as his colour, layer by layer to make them absolutely flat to the eye. Nicholson puts the paint on with a far freer brush. Most distinctly, Nicholson in his series of White Reliefs, in which he chiselled out the shapes into a plane of word, uses shadow and the presence of the handmade to give his pictures a quality of sculpture that the more purist Mondrian never sought.

And yet both artists were united in an exploration of what the abstract could achieve. And both were driven – embarrassing although it may be to declare now – by a profound sense in the spiritual capacity of art. Nicholson was a Christian Scientist, Mondrian had once signed up to theosophy. For them art, and the achievement of balance in it, was a calming and restorative process.

When Nicholson famously described himself on his first visit to Mondrian's studio in April 1934 as overwhelmed less by the works in progress than the atmosphere, he was speaking from the heart. The feeling in his studio, he reported, "must have been very like the feeling in one of those hermits' caves where lions used to go to have thorns taken out of their paws."

And then there was friendship. It's an area too little explored in the creative process. The history of painting in particular has come to be written in terms of rivalries – Michelangelo and Leonardo da Vinci, Picasso and Matisse. The best known friendship is the most spectacularly failed one, that of Van Gogh and Gauguin.

But creative friendship can be a supportive and refreshing factor even for the most different of temperaments. Looking at this flowering of talent, it's hard not to sense a feeling of mutual confidence in both artists. Nicholson, still in his thirties when they met, was growing frustrated with the Cubism he had espoused with such enthusiasm, and was still tempted by the figurative course he was later to follow. The support – and it was genuine respect from Mondrian, who pinned up photographs of his friend's work in his studio – of the well-established and respected (at least on the Continent) Mondrian must have been reassuring to him, particularly in following an abstract geometric abstract course.

Equally, Mondrian, a generation older, must have felt the energy and support of a younger artist whose work he approved and whose spontaneity and social connections he could warm to. Nicholson, a good socialiser, took his friend to where he could dance – a favourite pastime of Mondrian's although some partners derided his skills He also saw to it that he had a studio flat in Belsize Park close by Moore, Hepworth, Herbert Read and other like-minded artists. Mondrian, an urbanite by nature, liked London and its "bigness" and only left for New York when the bombs started to fall and St Ives and a retreat to the country seemed unappealing.

The exhibition ends with two supremely confident individual paintings by the friends, Nicholson's 1938 (White Relief) and Mondrian's Composition No 1, with Red. Both are studies of multiple vertical and horizontal lines, Nicholson's brought into relief by the shadow of his precise incisions, Mondrian's by the spacing and thickness of the black. The curators believe the two works may well have been completed concurrently in their respective and neighbouring studios.

One would like to think so. This is a warm as well as approachable show. The works, borrowed from a wide range of sources, may not prove a full dialogue between the two artists. But they certainly suggest a conversation and a mutual support which we can share. Another feather in the cap of a gallery that has made a consistent success of small shows centred on one of its own paintings (in this case the pitch-perfect 1937 (Painting) and building a concentrated theme around it.

Mondrian//Nicholson: In Parallel, Courtauld Gallery, London WC2 (courtauld.ac.uk) to 20 May