Their faces call out to us across two centuries. Sometimes they put us in our place with wrinkled lip and sneer of cold command, in the words of Francisco Goya’s younger contemporary Percy Bysshe Shelley in his poem Ozymandias; as often, they beguile or impress, vividly conveying intelligence, charm and sensuality.

Goya was a very great painter of portraits, as may be judged at the wonderful exhibition just opened in the Sainsbury Wing of the National Gallery and continuing into next year (January 10). If ever a show deserves to be called a ‘must see’, this one is it.

Never before has there been such a display, featuring almost half of the 150 or so surviving portraits completed during the long working life of the artist, who lived from 1746 to 1828 during tempestuous times reflected in other areas of his work.

A number have never been seen in Britain before. In this category is the amazing study (1797) of the Duchess of Alba, generously lent by the Hispanic Society of America, which has become the poster image of the show.

Depicted in classical simplicity, this mighty aristocrat is dressed in a black costume and mantilla, with a striking red sash around her waist.

Her authority is emphasised by her right hand pointing imperiously to the artist’s inscription on the sand beneath her, ‘Solo Goya’ (Only Goya). For years, it had been believed that the words proved an amorous relationship between artist and subject.

But the exhibition’s curator, Dr Xavier Bray, dismisses the notion. Writing in Goya: The Portraits (National Gallery, £19.95), he says: “That myth has been set aside by Goya scholars, and the inscription is now interpreted as the artist’s proud reference to himself.”

An important addition to the artist’s roll-call of patrons (among them the Spanish royal family), the impulsive and capricious duchess entered Goya’s life in an unexpected visit to his studio.

As he wrote to a friend: “The [Duchess of] Alba... barged into my studio yesterday to have her face painted.”

By this was meant not a study of her face but a painting on the thing itself, the application of make-up, as it would now be called. Another great beauty on view at the gallery is – and I pause before embarking on the full magnificence of her name – Dona Joaquina Tellez Giron y Alfonso-Pimentel, Countess of Osilo and Marchioness of Santa Cruz.

The somewhat daring study of 1805 (her 21st year) is one of a number of important pictures lent for the exhibition by the Museo Nacional del Prado. That the National Gallery’s new director Gabriele Finaldi had previously been the Prado’s deputy director for collections doubtless proved helpful in this area.

The marchioness, in fact, was married to the man (the Marquis of Santa Cruz) destined to become, in 1819, the Prado’s first director.

“This is a portrait in sensationally good condition,” writes Dr Bray, “on which is it possible to see the original energy and verve of Goya’s brushwork.

“It was a bold step for a young married aristocrat to be seen in a dress that reveals the anatomical position of her navel below her prominently displayed breasts to which attention is drawn by a seductive tendril of dark hair.”

It was in his royal portraits in particular that Goya managed to combine his insightful observation and technical refinement to create unique and memorable pictures.

Aspects of the sitter’s personality were conveyed by a subtle look or gesture.

Charles III in Hunting Dress (Duquesa del Arco) shows the wrinkled, weather-beaten face of a man famously considered ugly and not ashamed to be seen as such.

No more visually appealing was Ferdinand VII (Museo del Prado) in which can be seen the artist’s mistrust of a haughty monarch who abolished Spain’s liberal constitution and reintroduced the Spanish Inquisition.

A number of self-portraits on view. These include the remarkable study Self Portrait with Doctor Arrieta, 1820 (The Minneapolis Institute of Art). Goya is seen in the arms of the man who saved his life during a serious illness suffered when he was 73. It is a memorable tribute to the power of science.