This show of official royal portrait photography – the first exhibition at the newly renamed King’s Gallery at Buckingham Palace – could have been so stilted, yet isn’t. The secret of its success? It takes the photographers as seriously as their high-born sitters, and traces the trajectory of a medium over the past century, as immaculate soft-focus effects, achieved within the studio by practitioners with first names such as Bertram and Olive, gave way to something more intimate and informal.

Of course, Royal Portraits – which includes, among 160 vintage prints, several unseen images – is awash with glamour and familiar faces: how could an exhibition containing dozens of shots by Cecil Beaton be anything but? Its early sections are a numinous, natty haze of tulle and taffeta gowns, fur stoles, and peaked lapels; later, Princess Margaret – sometimes bare-shouldered, always brilliant-eyed – displays a film star’s smouldering poise. Likewise, Princess Diana, who appears three times: once, in playful maternal mode; twice, flirtatiously close-up. (Queen Camilla pops up in four photographs.)

It takes the King a little longer to demonstrate such ease in front of the camera. A double portrait by Beaton captures him as a chubby boy sitting beneath his angular father, who dwarfs him; delicately, a label refers to the “paternal dynamic”. Nearby, in a portrait released to mark his 18th birthday, he comes across as sweet but gawky.

Nadav Kander’s monumental headshot, though, commissioned by Time in 2013, and prominently displayed against a cardinal-red wall in the final room, is a persuasive vision of modern monarchy. In it, Charles (then still the Prince of Wales) appears considerably brisker and more at ease than he does in Jonathan Yeo’s painted likeness of him as a doddery regimental colonel drenched by a tropical crimson storm, unveiled earlier this week. Deftly, Kander ensures that his subject’s shirt, tie, buttonhole, and silvery hair all echo, and so enhance, his glittery grey-blue gaze.

Yet, the exhibition’s interest in photographers and their craft – its art-historical chops, in other words – also deserves respect. The curator, Alessandro Nasini, is mindful that photographs are objects with tangible properties, and finds room for unusual exhibits, such as a touched-up dry plate negative or a solarised print of Princess Elizabeth. Labels are rarely sycophantic, but point out subtle material details, such as the way that textured paper can give a print a “velvet-like quality”, or the fact that the “diamond dust” supposedly embellishing Andy Warhol’s screenprint of Elizabeth II is really “fine particles of crushed glass”. Blue squiggles overlaying the Queen’s face in Warhol’s image recall red annotations by Lord Snowdon indicating areas for retouching on a nearby proof of Princess Margaret. Celebrity is an artful construction.