The oldest guinea pig in English art, clutched by a solemn seven-year-old Tudor girl, will soon go on display at the National Portrait Gallery in London.

The little animal looks more content than its anxious owner, probably secure in the knowledge that it was unlikely to become her lunch, as it certainly would have done at home in South America.

The painting is believed to be by an anonymous Flemish or Dutch trained artist, much in demand among the English gentry for high-status portraits depicting every pearl and gold button.

It dates from around 1580, and is believed to be the earliest depiction of the animal in England. It was painted at a time when guinea pigs, tender chunks of protein in South America, were beginning to be imported by the Spanish as exotic pets for wealthy Europeans.

The identity of the three solemn children, magnificently and uncomfortably dressed at seven, six and five years old, is also unknown. The youngest is holding a goldfinch, popular pets with children because of their beautiful plumage, but often with religious overtones in portraits because the birds were also used in depictions of the infant Christ. The sturdy older brother was evidently judged too grown up at six for a pet.

The portrait has been borrowed from an anonymous private owner for the exhibition opening in October, Elizabeth I and Her People. The exhibition tracks changing fashion in portraiture, with images of merchants, lawyers, goldsmiths, butchers, calligraphers, playwrights and artists. It includes likenesses of the poet and preacher John Donne and Bess of Hardwick, who became steadily more wealthy through serial marriages and built her own palatial house.

The wealthy were also commissioning images of their children at a time when child mortality meant many would never reach adulthood: statistics suggest at least one of the solemn trio in the portrait would not have made it.

The exhibition will feature a positive menagerie of exotic and more humble animals, including an elephant on a family crest. There is also a ring in the shape of a grasshopper, and a purse fashioned as a frog. A recently discovered miniature of Elizabeth by Isaac Oliver shows her with a peacock.

Another shows her treasurer William Cecil, Lord Burghley, riding on a mule, a deceptively meek image of one of the wealthiest and most powerful men in her circle: he is recorded as relaxing from the cares of running the exchequer and a string of spies by riding around his extensive garden.

Elizabeth I and Her People is at the National Portrait Gallery, London, 10 October-5 January 2014. www.npg.org.uk