“Hapless woman! What a fate is thine!” The radical thinker Mary Wollstonecraft lamented her daughter's future. “I dread to unfold her mind, lest it should render her unfit for the world she is to inhabit,” she cried.

Can you wonder at this maternal anxiety? The well-born 18th-century woman was confined to a dreary drawing-room life. Hers was a world of tea and quadrille and decorous gossip in which supper with the parson could provide hours of discussion and the trimming of a bonnet become a matter of urgency.

As far as the life of the mind was concerned, it was death by embroidery. The intellect, much like the linen in a wedding trousseau, was best left unfolded. After all, a woman once married became a piece of property. And what husband wanted an opinionated wife? It would be as bizarre as a spaniel with a political point of view.

It was the bluestockings who first struggled free of this suffocating gentility. And these are the Brilliant Women whom the National Portrait Gallery now celebrates in one of the small but delightfully lively shows that it periodically tucks into a cranny at the end of a corridor. These compact exhibitions, cluttered with all sorts of intriguing bits and bobs, are not conventional crowd-pullers. But, exploring a few select pieces from the gallery's collection in the wider context of a handful of loan works, they are always informative and refreshing.

It is definitely worth buying the catalogue for this show - and not least for the vivid life stories of the characters that feature. They range from the society hostess Elizabeth Montagu, through the popular and prolific writer Fanny Burney, to Ann Yearsley, a poetry-writing milkmaid. Montagu described herself as “a Critick, a Coal Owner, a Land Steward, a sociable creature”. She lavished the money that came in from her husband's mines on cultural patronage, and “rescued” and then supported Yearsley, though the milkmaid's success was eventually to cause such anxiety (how could a creature of such lowly station cope with celebrity?) that they fell out scandalously.

Brilliant Women: 18th-century Bluestockings starts its story in the middle of the century, when, somewhere in the 1750s, a circle of intellectuals first met to debate in the salons of society hostesses. It took its name from the footwear of the botanist Benjamin Stillingfleet, who, apparently, turned up at one gathering still wearing his thick navy stockings instead of the acceptable white silk. Worst of all, his grand hostesses seemed quite unconcerned. It was the man's mind not his hosiery that they cared about.

From this founding moment, the show follows the tale of a feminist revolution into decades in which the learned creativity of women could be celebrated, in which ladies could swap social gossip for cultural patronage, could abandon their whist tables for library volumes and replace cotillion balls with intellectual debate.

It shows us a world in which women could be recognised as thinkers in their own right. They became authors, as in the case of the magisterial historian Catharine Macaulay, whose eight-volume History of England became a bestseller; or artists, as in the case of Mary Moser, flower painter and founder member of the Royal Academy (who is here charmingly captured at her easel by George Romney, proudly wielding the tools of her trade at a time when male artists, keen not to be considered mere craftsmen, would have painted themselves in court dress); or political philosophers, as in the case of Wollstonecraft, in whose study Talleyrand famously found himself sipping wine from a teacup.

The proudly pioneering and often stubbornly eccentric cast of this story is captured in portraiture - for all that several of them felt little inclined to waste precious time sitting. The professed repugnance of the writer and philanthropist Hannah More to having her likeness taken grew apparently greater as her life progressed. At the age of 76, increasingly aware of the urgency of her mission, she objected from a “moral point of view” that so much time out of “the fragment left” to her should be wasted in such a way. Nonetheless, an adamantly direct if unfashionably honest image of this “bishop in petticoats” did get painted to serve as inspiration to generations to come.

But don't be discouraged. This show is not just a panoply of hatchet-faced dowdies dragged up from the storerooms. There is a handful of fine pictures; the jewel among them, on rare loan from a private collection, being Allan Ramsay's portrait of Elizabeth Montagu, “the Queen of the Blues”, as Samuel Johnson (one of a significant supporting cast of male players) dubbed her. Ramsay brings a characteristic delicacy of touch and expressive vivacity to his image of this woman who was famously described as “brilliant in diamonds, solid in judgment, critical in talk”.

Other images, if artistically less fine, are still historically fascinating. A 1738 canvas of the poet prodigy Elizabeth Carter may look undistinguished. But once you understand how it embodies a public taunt to the misogynist Alexander Pope, it becomes riveting. The SwissAustrian painter Angelica Kauffmann ventures bravely into the lofty artistic territories of mythological painting (and offers a paean of praise to her own notable beauty on the way) by ostentatiously pinching a clearly recognised classical composition in her autobiographical The Artist Hesitating between the Arts of Music and Painting. A 1780 image of Hannah More is probably the first in which a woman is presented déshabillée in her study, and the startling Madame de Staël as Corinne shows us a woman as a Romantic genius for the first time.

This show, though small, has a satisfyingly broad sweep. Here are the intimate circles of mutually supportive friendship. A fiddly little friendship box, its surfaces decorated with miniature portraits, intrinsically captures a sense of intimacy. A private letter from the young Wollstonecraft to the ageing Macaulay has a moving enthusiasm. Wollstonecraft sees Macaulay as a mentor, she says, because she “contends for laurels whilst most of her sex only seek for flowers”. But, from the centre of small circles, the ripples of female enlightenment spread outwards, finding expression in a wider social, historical and political context. Against the increasingly confident background of an England that has won the war against France, that is acquiring new colonies and growing ever-more rich, the educated woman becomes an icon of patriotic pride, triumphantly celebrated in a highly significant allegorical portrait in which nine contemporary ladies pose as the classical Muses.

And yet the bluestocking occupies a precarious place on the stage. A host of satirists, misogynists and disapproving members of her own sex are always waiting to mock this insubordinate female from the pits. Towards the end of the century, in an England unsettled by the French Revolution, fearful of republicanism, the bluestocking was dropped. She had become a dangerous radical. The only safe form in which her feminist mission could persist was as a Cranford-style model of obedient Christian philanthropy.

This show captures a mindset as much as an 18th-century movement. It evokes an uneasy sense of the ambivalent feelings that the truly intelligent female can still provoke.

Brilliant Women: 18th-century Bluestockings is at the National Portrait Gallery, WC2 (020-7306 0055), from Thursday

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