Never mind the china shop — a huge frenzied bull is about to be unleashed in our National Gallery.

When this season's most excitedly anticipated blockbuster, Picasso: Challenging the Past, opens next week, the artist who saw himself as a big black Spanish bull will be thundering around among the Old Masters, tossing traditions about with his horns.

This show marks a landmark moment for the gallery as much as for the art-loving public. Normally one would expect Picasso to be shown not at the National Gallery but at the Tate.

Twelve years ago an agreement was reached between the two London institutions. The modern era, it was decided, began in 1900. Canvases were swapped. A Picasso still life from 1914 was sent off to Millbank while an 1890 Van Gogh landscape came over to Trafalgar Square. But now comes a new show that scuffs over that line in the sand. The arena of debate opens again.

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Nicholas Penny, the director of the National Gallery who, appointed only last year, is the inheritor rather than instigator of this potentially controversial exhibition, is keen to point out that no agreement has been broken.

“This show is a departure,” he agrees, “but the arrangements made between the two galleries referred to acquisitions rather than exhibitions. And our exhibitions policy is supposed to relate to our permanent collection — to complement and extend it.”

The Picasso certainly sets out to do that. The radical Spaniard was a fiercely competitive artist, and a preview allows The Times to see the sort of havoc his arrogant talent could wreak.

Here is Velázquez's iconic Las Meninas torn to pieces by a sharp Cubist vision, or Poussin's Rape of the Sabines thrown up in the air, Goya's languorous nudes trampled into big lumpy messes or Manet's Déjeuner sur l'Herbe skewered with his wit.

In 2002 Tate Modern put on a spectacular show that made explicit the direct and intensely creative rivalry between Picasso and his contemporary Henri Matisse. Chris Riopelle, co-curator of this new show, says: “But, because Picasso was so revolutionary as a painter we tend to forget that he had a very academic training.”

Now we are given the opportunity to observe him from another angle: watch him honing his skills, testing his power, pitting his wits against European traditions.

Picasso's images, for the most part, are loose interpretations rather than direct copies. In Paris (from where it travels) Old Master and Modern were hung side by side, inviting often reductionist comparisons.

The National Gallery wants to avoid this sort of “spot the difference” competition. Instead, it hopes to tempt visitors back up to the permanent collection to look at the sort of works the great Spanish radical would himself have seen on his visits to London in 1919 and 1950.

It hopes to use Modern outlooks to invite a fresh reconsideration of Old Masters. Was Picasso inspired by Rubens's Three Graces to try to capture three facets of the female form in one single figure, Mr Riopelle wonders.

He would certainly have made a beeline for the luscious Rokeby Venus, who reappears as a sort of archetype in his female nudes.

One of the most important things about this show, Dr Penny suggests, is that hung thematically — the self-portrait, the nude, the still life — many of the rooms present a sort of mini-retrospective. And on top of that they offer a classical yardstick against which to to measure Picasso's developments.

“Normally,” he says, “the Old Master wins hands down. This show will be most controversial in the sense that it should stir real critical debate of Picasso's stature. He's a great artist yes. But he's patchy too.”

Is Picasso all that he's cracked up to be? Next week the debate will begin. What is certain, however, is that after a lacklustre year for the box office the National Gallery is booming back with a blockbuster.

And who would blame the director if this whets his appetite for more shows of this sort?

Dr Penny is currently in talks with the Tate, trying to clarify the exact nature of the relationship between the two institutions. “Tate Modern is the national gallery of Modern art,” he says. “But Modern art in the future may be differently defined.”

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