In “Good Luck to You, Leo Grande,” Emma Thompson plays Nancy Stokes, a widow and retired religion education teacher who has endured a lifetime of erotic unfulfillment. Until today. As the movie opens, Nancy is arriving at a featureless hotel room to meet the sex worker she has procured for the evening — a last-ditch attempt at finding out what she’s been missing for the past 35 years.

Luckily, the male escort in question is Leo Grande, a dreamy-eyed, sensitive pleasure-giver played with silky self-confidence by newcomer Daryl McCormack. Viewers already rolling their eyes at what sounds like a dangerously cliched farce or hackneyed psychosexual mind game can be of good cheer: “Good Luck to You, Leo Grande” turns out to be a wise, amusing, unexpectedly touching exploration of human psyches, the bodies that house them and radical self-acceptance — by way of a literate two-hander executed by actors at supreme ease with each other and, by extension, their audience.

Thompson fans — and really, by now, who isn’t? — will already be sold on “Good Luck to You, Leo Grande” by premise alone: Nancy is a character the actress feels born to inhabit with her signature blend of vulnerability and pragmatism. First as a dutiful daughter, then as a wife, mother and teacher, Nancy has repressed her own desires her entire life; in less capable hands, she’d come off as pinched or pathetic. But Thompson imbues her with flint and knowing humor: She’s self-aware enough to know how ridiculous her predicament is but dignified enough not to be ridiculous herself.

Nancy and Leo’s first encounter goes well enough to lead to a second — and eventually two more — during which their explorations veer from the purely physical to the emotional and, inevitably, to an uncomfortable boundary violation. With his come-hither gaze, delicious Irish accent, easygoing physicality and heart-melting vocabulary (he drops the word “empirically” within seconds of walking through the door), Leo seems almost too good to be true. Which, of course, he is: McCormack plays Leo with such offhand spontaneity that the penny drops only gradually that he’s skillfully delivering a performance within a performance, as a man who is constantly crafting his persona for a living.

Because “Good Luck to You, Leo Grande” takes place almost entirely in the same hotel room over the course of several weeks, it could easily feel stagy or monotonous or cramped. But director Sophie Hyde, working from a smart, nuanced script by Katy Brand, provides just enough space and pace for Thompson and McCormack’s chemistry to combust, seemingly in real time. Working with cinematographer and editor Bryan Mason, Hyde avoids all the pitfalls that so easily could have toppled the setup: leering humor, stale jokes about aging, false epiphanies at the hands of a well-built young lover, a la Brad Pitt in “Thelma & Louise.”

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Which isn’t to say that “Good Luck to You, Leo Grande” isn’t funny, disarmingly honest or surpassingly sexy. It’s all of those things, thanks to Thompson’s and McCormack’s winning central performances and a filmmaking style that prioritizes genuine intimacy over the cosmeticized moaning and groaning that has passed for a Hollywood sex scene for years. When Leo shows up for their second appointment, Nancy crisply informs him that this time she’s brought along “a little bit of feedback” and a list of attainment goals. The fun of “Good Luck to You, Leo Grande” might be found in how they tick off those boxes, but the meaning of it is found by way of a clever, and ultimately moving, misdirect, expressed in the film’s final shot that, after an hour and a half of dialogue about varying sexual positions and proclivities, somehow feels like the biggest taboo of all.

It’s a revolutionary moment that shouldn’t be revolutionary at all. And yet it gives “Good Luck to You, Leo Grande” both its heft and its lift, leaving viewers with the sense that Nancy isn’t the only one who’s been liberated. When Gloria Steinem hit middle age, she said, “This is what 40 looks like.” This is what our movies — and movie stars — can look like, too, if they’re just given the chance.

R. Available on Hulu. Contains sexual material, graphic nudity and some coarse language. 97 minutes.

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