On paper, the concept of a portrait gallery sounds like Field Trip Hell. But actually, you’ll be surprised how the best works capture the sparkle of life behind history’s most charismatic shapers. Here, the names from your high school textbook flower into flesh-and-blood people, and the accompanying biographies are so sublimely evocative (Samuel Johnson is described as “massive, ungainly, plagued with nervous tics”) that subjects come alive.

The ancient kings and queens have the most heft, partly because it’s hard to wrap your brain around the fact that in many cases, the actual people posed in the same room as these very canvases. One of the most instantly recognizable paintings is the Ditchley portrait of Elizabeth I (room 2), in which the queen’s jeweled gown spreads like wings and Her Majesty firmly glares at the viewer under stormy skies. Right away, it becomes clear that many artists are slyly commenting on the disposition of their sitters. The troublesome Henry VIII is shown in several likenesses. One is a delicate 1537 paper cartoon by Hans Holbein the Younger (for a mural at Whitehall—a rare survivor from that palace), in which the king suspiciously peers with flinty grey eyes—hinting at a shiftiness that His Majesty probably couldn’t recognize in his own likeness, but that all who knew him feared (room 1). One painting of King Edward VI, painted when he was 9, is executed in a distorted perspective (called anamorphosis) that requires it to be viewed from a hole on the right side of its case (room 1). In 2014, the 1630s self-portrait of Van Dyck (room 15) was recovered from four centuries of private ownership for £10 million in patron donations of £1 to £20,000—the world’s most valuable selfie. You’ll also find George Washington (he was born an Englishman, after all), and one of the only authoritative images of Captain James Cook (room 14), who was so pivotal in colonial expansion. In room 12, look for the newly acquired Chevalier D’Eon (sometimes on loan), a male diplomat and fencing champion who lived as a woman in the late 1700s; in room 10, for the adorable little nose of William Hogarth in his terra-cotta bust; and in room 18, for the sketch of Jane Austen by her sister Cassandra—friends said it stank, but here it is. The Brontë Sisters appear together in an 1834 portrait found folded atop a cupboard in 1914; their alcoholic brother Patrick Branwell Brontë painted himself out but his ghostly image is eerily re-appearing (room 24). The genius of artist John Singer Sargent is immediately apparent in the 1894 likeness of poet Coventry Patmore (room 22); with just a few spare brush strokes, you feel like you know him.

Fortunately, the portraits don’t stop when cameras were invented. Margaret Thatcher, imperiously glaring over the grey gunwale of a dais at the Conservative Party Conference in Brighton, is Paul Brason’s fearsome and not-very-fond representation of the Iron Lady (1982, room 32); Princes William and Harry make appearances in a 2009 sitting (room 32), wearing the uniform of the Household Cavalry, and Beatrix Potter (1938, room 31), pictured in front of some sheep, looks as soft and kind as the gran you wish you had. Modern portraits (an impressionistic Ed Sheeran, anyone?) change often because there’s not enough room to show everything. Just about everything can be photographed (never with flash) or purchased as a poster in the gift shop.

The £3 audio/video guide starts out dull, but by the end, it uses archival recordings, which is cool, and there’s a $2 smartphone app (there’s free Wi-Fi) of the highlights. Bring kids; the desk lends free discovery trails for them.

Late Shift evenings (Thurs–Fri 6–9pm), with DJs, talks, live music, and sketching sessions, are great fun and a smart way to free up daytime hours to see more attractions. Also consider the pre-theater menu (£20 for two courses, £24 for three) served from 5:30 to 6:30pm in the rooftop Portrait Restaurant ([tel] 020/7312-2490), which has a breathtaking view of Nelson’s Column and Big Ben’s tower—it’s better than the National Gallery’s.