‘Upstairs Downstairs’ begins Sunday on PBS and continues on April 17 and 24. (Jane Hilton)

In the afterglow of “Downton Abbey” and “The King’s Speech,” it would seem like a fortuitous moment to blow the dust off “Upstairs Downstairs,” the beloved British drama about 20th-century Belgravian uppercrusties and their loyal servants — a show that became a PBS “Masterpiece” juggernaut for some 70 episodes and proved deeply satisfying to Viewers Like You until it went off the air in 1977.

But this new, more mild “Upstairs Downstairs,” which makes its American premiere on PBS on Sunday night, is a three-part epilogue that feels more like an unfinished afterthought.

It returns us to Eaton Place six years after the last of the Bellamy family moved out and the staff was dispersed to other postings. It’s now 1936, and a young diplomat, Sir Hallam Holland (Ed Stoppard), has returned to London with his wife, Lady Agnes (Keeley Hawes).

The search for the perfect home leads the couple to 165 Eaton Place, which hasn’t held up well, acquiring about 40 years’ worth of dirt and disrepair in a fraction of the time. Lady Agnes is nevertheless enchanted and sets about bossing workmen around in an extreme makeover. Sir Hallam’s opinionated and eccentric mother, Lady Maud (Dame Eileen Atkins), moves in for a permanent stay, after decades of living abroad. She brings along her aide, Amanjit Singh (Art Malik), and her pet monkey, Solomon. Lady Agnes’s conniving sister, Lady Persephone (Claire Foy), also arrives and immediately causes a ruckus.

For her domestic staff, Lady Agnes turns to an employment agency run by Mrs. Buck. That would be the same Mrs. Buck who toiled for the Bellamys as a parlormaid, the same Mrs. Buck played by the same Jean Marsh who co-created and starred in the original series and now acts as a bridge between eras.

Mrs. Buck takes the housekeeper job herself and assembles a staff, and thus “Upstairs Downstairs” sets about reaching for something that’s unfortunately no longer there. In a way, this sense of the fleeting has always been the narrative subtext of such tales — not only in the original “Upstairs Downstairs” but also in “Downton Abbey” and a hundred other period dramas: Those who serve and those who are served struggle to absorb the subtle social upheavals around them. As before, this is a story about employers and employees remaining affectionately and emotionally codependent on one another, safe within the fortress of proper English manners.

Fans of the original can happily swim in the drama, details and costuming — as well as subplots and historical cameos that reference fascism, Hitler, Wallis Simpson and royal abdication — but sooner than later, something about this “Upstairs Downstairs” feels cheaper and less full than a true reboot ought to feel.

Only near the end, when a star is planted on the Hollands’ giant Christmas tree in the foyer (and warmth once again transcends the class divide), could I pinpoint where I’ve sampled this sugary aftertaste so many times before: It’s less like a quality period piece and more like a quickie Hallmark special.