The vast smorgasbord that is the British Museum offers too many riches and distractions to count for the history buff. But if you’re into archeology at all, the temptation is great to give the Elgin Marbles and the like a pass and make your way straight to room 141, to the treasures of Sutton Hoo.

“The Dig” is a warm, stately and beautifully-acted drama about how this Anglo Saxon era burial treasure was unearthed, a tale given weight, poignance and urgency by the events hanging over that dig. World War II was looming, giving this “amateur” unearthing in Suffolk a somber tone and need for speed.

They’re called “salvage digs” these days, a somewhat rushed job because something is coming — usually new construction — threatening whatever you hope to find with the risk of being “lost forever.” I took part in one as a teenager, a Native American village in my hometown that would be destroyed by an expansion of a sewage treatment plant.

Imagine that situation with the added menace of a World War on everybody’s mind.

That’s just one of the ticking clocks Edith Pretty (Carey Mulligan) internalizes when she offers a job to “excavator” Basil Brown (Ralph Fiennes). She and her late husband bought their land with a notion of finding out what’s in these mounds on the property. And after some haggling over wages, Brown agrees.

It’s 1939, and the lady of the house won’t be digging herself. She’s too frail. But she can commission this dig, on the cheap, and figure out what previous digger King Henry VIII never did. What’s under all that dirt? mounds?

Her inquisitive, comic-book fan little boy (Archie Barnes) will be under foot, literally. He offloads his entire brain’s supply of questions on Brown while wearing (literally) a tin foil hat and star-bedecked bedspread he treats as a cape.

Mrs. Pretty might be looking to leave her mark, lamenting an academic life she never had, or might be fulfilling a dead husband’s wishes. Brown is an autodidact — self-trained — and a veteran of such digs. Academia and the local museum toffs regard him as a laborer, someone whose value they don’t appreciate until he leaves them for her.

Both are looking for validation, and she has “a feeling” about this biggest mound, about “the dead and what they leave behind.”

Warplanes roar overhead on training missions, soldiers muster everywhere and the wireless crackles with news of the escalating crisis on the continent. But Brown, following the boss’s hunch, continues to dig in the dirt and mud under overcast skies. His own hunches, flying in the face of the “experts” who figure their Roman villa dig across the county is more important, have the promise of “This changes everything.”

But if it does, you can be sure those with degrees will rush in, led by British Museum archeologist Phillips (blustering Ken Stott) and take over and take the credit while they’re at it.

“You men there, finish up and then don’t move ANOTHER PEBBLE!”

That allows more characters to be introduced, the professorial Piggott (Ben Chaplin) and someone who might well have been his student, his new wife Peggy (Lily James).

Her arrival, summoned by Phillips as well, provides the film’s best sexist joke. As fragile as this long-rotted-away ship is, he needs someone “light” to get down there in it for the fine-work required.

Director Simon Stone (“The Turning”) and screenwriter Moira Buffini (the Mia Wasikowska “Jane Eyre” and “Tamara Drew”) cloak this story in deaths past and deaths sure to come, in class snobbery and curiosity. And then they toss in a hint of romance.

The late second act new characters and incidents associated with them give the film more of a fateful World War II romance touch. They also slow it down.

“Stately” implies the pacing is slow, and “The Dig” generates a feeling that it’s taken on a few too many issues and messages for its own good. “Class” and “credentials” snobbery are the heart of the story, and with all this added-on stuff, there’s barely time for our heroine to stand up for our hero against the snobs of academe.

But Mulligan — drawn, wan and yet steely here — and Fiennes’ lightly-laid-on sturdy working class polymath turn make “The Dig” touching and richly rewarding, as entertaining as any movie about archeology could be without a bullwhip.

MPA Rating: PG-13 for brief sensuality and partial nudity 

Cast: Carey Mulligan, Ralph Fiennes, Lily James, and Ben Chaplin

Credits: Directed by Simon Stone, script by  Moira Buffini, based on a book by John Preston. A Netflix release (Jan. 29)

Running time: 1:53