Helen Mirren has played queens so often that she’s likely to earn an honorary throne at Buckingham Palace.

She played Queen Elizabeth I in the HBO series “Elizabeth I” in 2005 and then, in a one-two punch, played Queen Elizabeth II twice — winning a Best Actress Oscar for Peter Morgan’s “The Queen” in 2007 and then scooping up Olivier and Tony awards for Morgan’s play “The Audience” in 2013 and 2015.

Now she’s back as the titular “Catherine the Great,” premiering Monday (10 p.m.) on HBO.

Mirren, 74, turned her regal gaze east to her father’s Russian homeland — her given name is Helen Lydia Mironoff — and let it be known that she wanted to play Catherine the Great, the German-born Russian empress who ascended the throne after staging a coup against her feckless husband, Peter III, whom she describes as “the ugliest man east of Berlin.” She ruled from 1762 to 1796 — the longest any woman ruled that vast country.

“For Catherine to have the additional descriptor ‘The Great,’ like ‘Peter the Great,’ these people made huge, substantial changes in the history of their countries,” Mirren tells The Post. Among Catherine’s accomplishments was the establishment of a state-financed school of higher education for girls called the Smolny Institute for Noble Maidens and bringing smallpox inoculations to two million of her subjects.

“The world she inherited was unbelievably violent,” Mirren says. “The struggle for power was brutal. She had incredible courage. You can’t get your head around the vastness of the Russian landscape. The many, many languages and cultures that are incorporated into what is Russia. The Russian personality, the character is very, very deep.”

“Catherine the Great” lists Mirren as an executive producer, allowing her to choose the screenwriter. At the top of her list was Nigel Williams, who wrote “Elizabeth I” for her nearly 15 years ago. She knew he would combine historical accuracy without sacrificing personality. “He’s clever and creates dialogue that’s accessible,” she says, “and not just ‘My Lord.’ ”

Mirren says playing yet another queen never gets dull. “I like to discover elements of their personality. It’s a great process and not one you can find easily,” she says. “Whenever one of these roles is available, you grab it.”

Once seized, Mirren imbues the monarch with a blend of imperiousness, sensuality and cunning that’s underscored by an intelligence that set Catherine apart as the smartest person in the palace. She did not suffer fools, telling one beggar, “It’s a mistake to ask rich people for money. How do you think they got rich? By not giving it away.” Shooing one lover out of the royal bed chamber, she commands, “Get your clothes on now. I have to work.”

She meets her match, so to speak, in military leader Grigory Potemkin (Jason Clarke), a fearless sort who fought the Turks and helped Catherine expand the empire into Crimea and the Ukraine.

“Potemkin was the love of her life,” she says. “She adored him. Their relationship only lasted four years as a couple. He was conquering lands for her. They became consciously uncoupled. They realized they were never going to be an old married couple together. In an ideal world, she would have married him, but if she married anyone, they would take the power.”

The series’ four episodes cover the 34 years of her reign (Catherine died at age 67) and were filmed in palaces in St. Petersburg and Latvia. Mirren’s husband, director Taylor Hackford, recognized the interior of one orthodox church as a location he scouted before shooting the 1985 film “White Knights.” “The Soviets used it as an ice-skating rink,” Mirren says with a laugh.

Mirren’s royal mien may make her a natural for playing monarchs, but she says the key to playing a queen from another century for a modern audience is “to humanize these people. That’s done with a combination of the writing and the direction and the acting. It’s a question of pulling the audience into the story.”

That said, the question inevitably arises whether Catherine will be her last queen. Is Mirren really ready to lay down her scepter? “Yes,” she says. “Probably.” Then she pauses. “Maybe there are a couple more.”