“Cradle to Grave,” a BBC series making its American debut online today on Acorn TV, is a highly likable example of the my-magical-childhood sitcom, a first-person exercise in narrated nostalgia that recalls “The Wonder Years,” “The Goldbergs” and Chris O’Dowd’s (even better) “Moone Boy.”

The show is based on a memoir by Danny Baker, a British radio and television personality who writes the show with Jeff Pope (“Philomena”) and is played as a 1970s teenager by a charming young actor named Laurie Kynaston. The Bakers — Danny; his older brother and sister; and his parents, Spud and Bet (Peter Kay and Lucy Speed) — live in a working-class, pre-gentrified South London where your own wits get you from cradle to grave, with no help from the government.

For those old enough to remember, the 1970s references are thick and delicious, and sufficiently accessible for American viewers — platform shoes, enormous VCRs, the discovery of wine by non-Mediterranean middle-class households. Consistent instant gratification is provided by the soundtrack, which ranges from Led Zeppelin to the Spinners to pop relics like David Essex (“Rock On”!), with more contemporary interjections by Chris Difford and Glenn Tilbrook of Squeeze.

The key thing about the time period, though, is the transition taking place from a hardscrabble postwar society to the new, button-down London. “Sorting something out,” in ways mildly to thoroughly criminal, is a way of life for Spud, who works on the docks. An early montage shows how merchandise of all sorts — pillows, shoes, puppies — finds its way from the holds of ships to the Baker house.

Much of the show’s humor and pathos (because this kind of series comes with a heavy dose of sentimentality, and “Cradle to Grave” tips to that side) is generated by Spud’s losing battle against the economic realities of globalization, as shipping moves to the continent — to Rotterdam, in the Netherlands, and to Hamburg, Germany — and the dock workers are offered increasingly attractive buyouts. Exploring alternatives, he moves even further back on the historical scale, trying his luck as a rag-and-bone man. With his expansive personality and gift for gab, he’s a natural at collecting and selling junk, but as he discovers when he tries to make a killing in horse manure, it’s too honest a profession for him.

Danny, a high schooler, is nominally the central character, and much of the plot is taken up with his efforts to free himself of his virginity, first with a neighborhood girl and then with a worldly photography teacher. Kay dominates the show as Spud, however, both because of his generous, blustering performance and because Spud is the one character Baker and Pope have fully imagined. The other Bakers are more standard-issue sitcom types, but the usual excellent British cast makes everyone on screen believable.

“Cradle to Grave,” with its loose, episodic structure (there’s a lot of “I remember when …” and “So there I was …”) and its wistful glow may seem beside the point at a time when the metacomedy and the harsh noncomedy are in ascendance. But if your diet allows for the occasional toad-in-the-hole, it could be your dish.