The English visitor to America has been speaking for several minutes when he becomes aware that his audience is staring at him, oblivious to the content of his speech. The American shakes his head in wonderment. Then comes the familiar line: "I looooove your accent." The Englishman realizes -- too late -- he's face to face with an Anglophile.

"People like to hear the accent," says John Hughes, press secretary at the British Embassy. "They say, 'Just keep on talking, keep on talking.' "

"They ask you to repeat yourself," says Englishman Jim Mitchell, who has lived in the United States for 21 years. "And then they say, 'Cor, I'd love to listen to you all day.'. . . They keep on and on, and you think, 'Am I going to get away?' "

For a country that threw off the yoke of the British Empire, there are an awful lot of loyalists around. Call it obsession with royalty, or tradition, or a search for roots, but it's thicker than serf's hosiery in this town. Just how many Anglophiles there are, flicking through their Burke's Peerages, talking (over high tea) about when She last changed her hair and when He last played polo (and isn't it a shame about the Younger Brother), cannot be determined. But this week, you're sure to see a Brit-loving quorum, as the Royal Couple visits Washington and the hyperpromoted "Treasure Houses of Britain" exhibition at the National Gallery of Art.

"We're absolutely inundated with telephone calls. We haven't even had a chance to count them," said a spokeswoman at the British embassy. "They're wanting to know the schedules of the couple . . . where they can see them . . ."

Tuck the Constitution away in a dusty cupboard in the basement of the Archives this week. The legacies of independence brothers Thomas Paine and Thomas Jefferson will be overshadowed as adult Americans enter the Court of St. James's world with heads bowed and eyes aglow. There'll always be an England. In America.

"What disturbs me," says Judith Martin, otherwise known as Miss Manners, "is that, while I think it is appropriate for us to welcome all foreigners with dignity, courtesy and friendship, I don't think we need reverse the outcome of a small war we fought with these people and go back to the idea that they are by birth more superior . . . I thought we had certain principles of equality which preclude bowing -- literally and figuratively -- before human beings, and I'd like to see the dignity of that reestablished."

The Anglophilia in Washington, says Martin, is an "obsequious demeanor, which I think is very un-American."

It is not easy to preserve one's democratic tenets. American cinema has deified, romanticized and wrapped British culture in ceremonial bunting. Imagine what would have happened to the careers of Robert Newton, Basil Rathbone, Ronald Coleman, Trevor Howard, Sir Laurence Olivier, Sir Alec Guinness, Sir John Gielgud and Sir Ralph Richardson (the list is endless) if they had been born with, say, a thick Brooklyn stress to their syllables.

And what would cinema be without such celluloid staples as the British epic (from "Mutiny on the Bounty" to "The Man Who Would be King"), the British butler (that classy plebeian in patrician's clothing), and that familiar character constantly hanging around street lamps -- the British fog.

Public television has all but Lloyd's of London insurance for the British accent. PBS would have been in real estate long ago if not for its knowledge of the irreducible formula: Import 12-part dramas where people in period flannels (a cricket bat and Pimm's Cup must be within comfortable reach) spend much time in drawing rooms discussing The Empire (which has been crumbling for years, but never quite topples). And make sure Alistair Cooke is comfy by the fire. The critics will love ya. . .

You might want to test your Anglophiliacal level by asking yourself the following questions. And, in the interest of science, be brutal:

*Do you have a weakness for Marmite or Chivers marmalade? In fact, do you stalk the delicatessen section at Safeway for foodstuffs labeled, "By Appointment to Her Majesty . . ."?

*Does Benny Hill make you laugh?

*Are you capable of eating fruitcake?

*Does Robert Morley strike you as endearing?

*Do you sneak the words "whilst" or "bloody" into conversation whenever possible?

*Do you like to go "on holiday?"

*Have you seen "Lawrence of Arabia" more than twice?

*Did you save the newspaper clippings showing President Reagan riding on horseback with the queen?

*Do you know the difference between steak and kidney pie and steak and kidney pudding?

*Do your associates have last names such as Temperton-Cottrell?

*Whilst on holiday abroad, does the thought of riding in a London cab make you tremble?

*Did you watch the Royal Wedding in its entirety?

*Do you refer to galoshes as "wellies?"

*Do you own Toby mugs?

If you answer in the affirmative to all these questions, chances are you have chronic Anglophilia and you will be at one of the welcoming parties for the Royals; or, if your finagling skills aren't what they used to be, you'll be outside in the driving rain, waiting to catch a glimpse of them. And of course, you'll be girded in mackintosh and wellies.