It doesn’t look like a building that was completed under cost-cutting constraints, in the face of the stock market crash of 1929.

You enter 3100 Massachusetts Ave. NW through imposing wrought-iron gates, go under a porte-cochere and up a double staircase decorated in the 18th-century tradition of English country houses with portraits of the great and good, drawings of flora and fauna, and views of cities, cathedrals, castles. From there is a breathtaking 165-foot East-West vista, past the ballroom’s glittering chandeliers and marble columns.

But if you’re invited to the British ambassador’s residence, while you’re waiting in the receiving line, walk over and knock (discreetly) on one of those columns. They look like Siena marble, but they’re faux. They’re scagliola! — the result of a 10 percent cut imposed by the British Treasury in 1928 after architect Sir Edwin Lutyens’s plans for a purpose-built embassy in Washington proved too pricey.

Even with cheaper materials (slate instead of black marble for floor tiles, and “distemper” in the servants’ quarters, which sounds like a dog disease but is a kind of paint), the residence was described by The Post in 1929 as “the finest Embassy in the world” and “a home fit for a king.”

It’s also the closest thing that Washington has to Downton Abbey.

“I hadn’t thought of it like that,” says Lady Westmacott, the ambassador’s wife, who would much rather be called Susie. Unlike Lady Cora, who uses Downton to entertain in her family’s self-interest, Susie Westmacott lives in an upstairs apartment in a house designed to promote a whole country’s self-interest, playing host to about 10,000 visitors at official functions every year, as well as welcoming hundreds of overnight dignitaries.

It is a “building that works very hard,” says Westmacott, who is inviting in more eyes with the publication this month of the lavishly illustrated book, “The Architecture of Diplomacy: The British Ambassador’s Residence in Washington.”

Lutyens designed the building to resemble an English country house, but it functions “almost like a boutique hotel” and is run by a residence manager, Westmacott says. The diplomatic offices moved out of the building’s front wings in 1960 to the concrete-and-steel chancery just to the north, but on any morning in the residence, there could be simultaneous breakfasts in the morning room, the dining room, the anteroom and the ballroom, not to mention the possibility of trays being carried upstairs, where Lutyens arranged for eight bedrooms off one corridor. The most elaborate room, where princes and prime ministers sleep, has a sitting room — another potential breakfasting spot.

Want more evidence? Downstairs, off a surprisingly small kitchen, 18 toast racks are hanging on hooks in the silver vault alongside gravy boats and salvers. (For those unschooled in the eating of English breakfasts, a toast rack is designed to hold slices of toast to attention in the morning — separate, upright and therefore crisp.)

How it all began

“The Architecture of Diplomacy” is not Westmacott’s first book project. She was the impetus behind a coffee-table book about the chef at the British embassy in Paris, where her husband, Sir Peter Westmacott, was ambassador before coming to Washington, as well as a volume titled “The British Ambassador’s Residence in Paris.”

The new book is a substantial work of scholarship that draws on historical correspondence, as well as being scrupulously devoid of news. Don’t expect tales of celebrity slip-ups on the front steps or spy scandals here. Instead, there is a wealth of architectural and diplomatic history, supported by sumptuous archival and contemporary photography.

“You are overwhelmed by the architecture of this building,” says Westmacott over tea in the light-filled drawing room, where six huge sash windows offer spacious views over the lawns, which are also reflected in a pair of carved wall mirrors.

Two years ago, Westmacott approached Anthony Seldon — a British schoolmaster who has authored biographies of recent prime ministers, as well as acting as historical adviser to 10 Downing Street — to write the text. He was joined by Washington-based political historian Daniel Collings. The foreword is by Prince Charles, for whom Peter Westmacott worked as deputy private secretary in the early 1990s. Funding came from the Campbell family (of the Campbell Lutyens investment firm). And any profits from the $65 book will go to Help for Heroes, a British charity that supports wounded soldiers. (The publication has ruffled a few transatlantic feathers: Local architectural historian Jane Loeffler, author of a book about U.S. embassy design overseas titled “The Architecture of Diplomacy: Building America’s Embassies,” complained to Peter Westmacott about the British book’s title.)

Seldon’s text sets the creation of an embassy against the history of Anglo-American relations. When it was newly independent, the United States was a bit player on the world’s stage, deserving only a “legation,” and Britain’s early envoys were mere “ministers,” occupying rented digs around Washington and later constructing a building at 1300 Connecticut Ave. NW.

With the designation of an official ambassador in 1893 came the need for a new building. The site chosen in 1925 — across Rock Creek Park and close to the Naval Observatory — was “out in the boondocks,” Susie Westmacott says. Construction was complicated by conflicts with U.S. labor unions and the deteriorating economy.

In spite of the scagliola and the distemper, Lutyens’s architectural ambitions left no money for the garden. A group of British subjects came to the rescue with 10,000 pounds — enough to finance lawns and flower beds and also a tennis court and swimming pool (although without the temple Lutyens had dreamed up).

Still, the building disappointed its early occupants, who had to cope with doors that swelled shut in the Washington humidity and an undanceable ballroom floor. The American wife of Sir Ronald Lindsay, the first ambassador to take up residence in 1930, complained to Lutyens: “We are dizzy with confusion, deafened by noise, poisoned by flies, exasperated by ineptitudes and overrun by rats.”

‘The queen is everywhere’

With a master’s degree in the history of art and a background working at the Freer and Sackler galleries, Westmacott takes delight in pointing out Lutyens’s touches of humor: a capital with no column to support it; tiny human figures holding back the shutters. He proves to have been something of a slave to symmetry: After knocking on the faux columns, try finding the faux window on the grand staircase and the faux doors along the main corridor, which open onto blank walls with a row of hooks.

There are also countless reminders that Britain remains a monarchy.

“The queen is everywhere,” says Westmacott, leading a tour of the building.

She’s larger than life in the ballroom, where a luminous likeness by Andy Warhol hangs over the fireplace.

There she is again, in two giant frames in a behind-the-scenes office where the butler — a far more dashing figure than Downton’s Mr. Carson — is busy.

And the queen is in the pantry, reigning over a huge cabinet of glasses, ready for receptions.

The queen doesn’t sleep here when she visits Washington. She stays at Blair House and entertains at the embassy, where she gives so-called “return dinners” for the U.S. president. Buckingham Palace provides the menus — still printed according to diplomatic tradition in French.

The challenge for 21st-century residents is to retain some of that rarified atmosphere while opening up to more people.

On one of the first warm days of spring, several volunteers are out helping the three gardeners pull weeds, plant lettuce and herbs, and spruce up the herbaceous border for the European Union open house on Saturday, when as many as 10,000 people may walk through the building and its grounds. This year, after an unusually inhospitable winter, there’s a worry that the English roses won’t bloom in time.