One reason behind the National Gallery's new exhibition of Turner and Claude Lorrain is to reclaim the British artist for the gallery. It's easily forgotten that the Turner bequest to the nation was put with the NG long before the Tate was hived off, taking it with them. And it is in Trafalgar Square not Millbank that two of his works are shown, as he had wished, side by side with the French 17th-century landscape artist whom he so worshipped.
The other reason is to examine that relationship. That is no surprise. On first seeing a Claude masterpiece, in 1799, the young British watercolourist is supposed to have burst into tears, exclaiming that these were works "beyond the power of imitation". The story is probably apocryphal. But it expresses an undeniable truth: that Turner was above all obsessed with light and it was seeing the works of Claude that freed him to pursue his constant attempts to delineate it.
Look at the two great "Altieri Claudes" brought to England to great acclamation by the extravagant figure of William Beckford – Landscape with the Father of Psyche sacrificing at the Temple of Apollo, and Landscape with the Arrival of Aeneas before the City of Pallenteum – and you are immediately reminded of dozens of Turner oils. What Turner saw, and what he studiously noted in a sketchbook of the time displayed nearby, is partly the composition of receding landscape framed by buildings and trees, and partly Claude's unique way of depicting light at sunrise or sunset, bathing the landscape in its warmth.
It's a combination to which Turner returns again and again, not least in the two paintings he asked to hang next to Claude's, Dido building Carthage (1815) and Sun rising through Vapour: Fishermen cleaning and selling Fish (ascribed to before 1807). Look at these, as Turner intended, next to Claude's Seaport with the Embarkation of the Queen of Sheba and Landscape with the Marriage of Isaac and Rebecca, both from 1648, and you see the same balance of mass between left and right, the same bend of the river and vertical of buildings and the same use of the sun in the centre of the picture to suffuse light throughout.
But look more carefully and you see a different sensibility in the young man's homage to his idol. Even in the two seaport scenes, seemingly very alike, Claude gives his building – as his figures – a statuesque concreteness, while Turner embraces them into the natural world around. Where Claude seeks a flat and shining paint surface, Turner uses the brushstrokes themselves to imbue his picture with life.
Comparison is at the heart of this show but also its weakness. By displaying Turners with similar composition to the Claudes on show, it invites the viewer to look for the similarities between the two and even to guess which is which. The message, and it's hardly a novel one, is that Turner continuously drew on Claude's inspiration even in his later pictures of the 1820s and 1830s. The effect, however, is both repetitive and in a way belittling to both artists, with Claude made to look limited and Turner to look derivative.
But it wasn't like that, at least so far as Turner was concerned. Profoundly influenced by notions of the "sublime" and the technical advances of his time, he was driven by more than just a desire to recreate the grand portrayals of myth and history that his contemporaries so valued in Claude. Where Claude wished to achieve the idyllic, Turner wanted to delineate the effects of light and atmosphere and the wonder of nature itself. Where Claude sought harmony, Turner sought dissolution.
The National Gallery tries to take this into account by showing how Turner recognised industrialisation and modernity in his landscapes. But it was more than a matter of recording novelty. What fascinated Turner was the atmospheric effect of furnaces and steam. The artist who rushed out into the Thames to sketch the Houses of Parliament on fire, would have been there recording the effects of the first atomic-bomb tests in America.
There's an extraordinary picture on show, Regulus, of 1828, a reworking of Claude's Seaport with the Villa Medici, which Turner himself revised in 1837 to remake the sun into the fiercely dazzling light that the Roman hero Regulus would have faced when his eyelids were removed by the Carthaginians. The rapid intensification with white shows an ambition never shared by his Baroque exemplar. And then there are the astonishing series of unfinished late canvases from images in his "Liber Studiorum" painted with Claude in mind, but in a different world of reach and technique.
Of course Turner did paint a lot of works with a nod to Claude, many of them rather too classical for modern taste. But to tie him in a harness with his idol leaves out what made the British master so daring and so advanced in his development. There are some real masterpieces on show, not least Turner's Keelmen Heaving in Coals by Night, a work of breathtaking brilliance on loan from the National Gallery in Washington and worth the price of entry alone.
The last room, devoted to Turner's bequest, the attempts by the family to stop it and the time when the Gallery declined Turner's wish for joint hanging on the grounds that he was now so admired he didn't need the cachet of Claude, is most entertaining.
But, coming so soon after the exhibition of "Turner and the Masters" at the Tate last year, the Ashmolean's extensive showing of Claude in Oxford and the current exhibition of his near-abstract works at the Turner Contemporary in Margate, it is difficult to see what the National Gallery was trying to achieve. If the point is simply Turner's debt to Claude, then you might just as well go to the gallery in normal times and seeing the two hung side by side, as Turner wanted, for free. The Turner exhibition that really needs to be mounted is an examination of his influence on the artists who came after him. We may get a glimpse of that when Tate Liverpool puts on its joint exhibition of Turner, Monet and Cy Twombly in June.
'Turner Inspired: in the Light of Claude', National Gallery, London (nationalgallery.org.uk) to 15 June