A painting of three of 18th-century society’s most glamorous and notorious women, including Georgiana, Duchess of Devonshire, as witches from Shakespeare’s Macbeth, has been acquired by the UK National Portrait Gallery.

The work will go on show in the gallery’s first exhibition devoted to 18th-century actress portraits.

The First Actresses: Nell Gwyn To Sarah Siddons, includes 53 portraits of actresses by artists such as Joshua Reynolds and Thomas Gainsborough.

The newly-acquired portrait shows two of the most famous political hostesses and society beauties of their day – Georgiana together with Elizabeth Lamb, Viscountess Melbourne – gathered around a witches’ cauldron with their friend, the sculptor Anne Seymour Damer.

It was painted in pastel in 1775 by Daniel Gardner and has been allocated to the National Portrait Gallery from a private collection in lieu of inheritance tax.

Georgiana, daughter of the first Earl Spencer, married the fifth Duke of Devonshire and was one of the greatest celebrities of her day and at the apex of Whig society.

Played by Keira Knightley in the recent film The Duchess, she had a daughter from her affair with Charles Grey, the Second Earl Grey.

Gill Perry, co-curator of the exhibition and professor of art history at the Open University, who has been studying the lives and reputations of the stars, says there was always endless ribald speculation about their sex lives – illustrated by many cartoons in the show – and a widely-held belief that most of them had worked their way up from very low origins if not outright prostitution. In fact, many came from irreproachable backgrounds, some made spectacular marriages, and others saved and invested their earnings and became producers and playwrights when their looks faded.

The exhibition runs from October 20, 2011 to January 8, 2012.