They were the ideal couple: old friends, mutual admirers and people who speak the same language in more ways than one.

The host was a former actor who had become president of the United States, his guest of honor a former scientist who had become prime minister of Great Britain.

"I've been a fan of Margaret Thatcher's since I met her 10 years ago and right after that I said she had to be prime minister," Reagan told reporters last night.

Thatcher complimented Reagan on his "massive victory" last November and gracefully turned the background music for last night's White House dinner into another compliment.

"I thought as I heard that song, 'I'll Be Seeing You in All the Old Familiar Places,' this is quite a nice, old, familiar place in which to see you, Mr. President," she said over toasts. "And I hope we'll be able to sing that song for very, very many years."

The reunion signaled the Reagans' debut as hosts for a state dinner although there was some discussion about whether that term really applied. The State Department called it an "official" visit since Thatcher is a head of government, not a head of state. The White House decided that since there are so few heads of state, a head of government can be accorded a state dinner.

There was also some confusion on another matter of protocol: Have the Reagans been invited to Prince Charles' forthcoming wedding or haven't they?

At first, standing alone with reporters in the Great Hall, the president said they had been invited and he hoped they would be able to attend. A little later when he had rejoined the first lady, he repeated it.

"I thought we had," he said, glancing at his wife for confirmation.

"No," she said, shaking her head.

"Oops, change of signals," said the president.

Earlier, when the time came for toasts, the president raised his glass not to his guest but to "Her Majesty, the Queen." Heavy on references to Anglo-American partnership, he called it "vital to the preservation of human freedom." Turning to Thatcher, he said, "It's well known that I share many of your ideals and beliefs."

In her reply, Thatcher gave a rather detailed presentation of those conservative political beliefs.

"You and I, Mr. President, believe in strong governments in areas where only governments can do the job, areas where governments can and must be strong, strong in the defense of the nation, strong in protecting law and order, strong in promoting a sound currency," she said. "If we do these things very well we shall indeed be leaders of strong government doing the things that only government can do."

During the brief wait at the top of the White House steps, while Thatcher's limousine was coming around the long driveway, Nancy Reagan shivered noticeably in her eight-year-old Galanos gown, which offered only two ribbons to protect her shoulders.Thatcher looked a lot warmer in a long dress and jacket of black velvet. The prime minister's arrival was signaled well ahead of time by the shouts of a group of Irish demonstrators on the Pennsylvania Avenue sidewalk. Meanwhile at the back door, formally clad guests were coming in accompanied, as in past administrations, by the strings of a solo harp played by a woman marine. The guest list was developed several weeks ago in an intensive 45-minute consultation between Nancy Reagan and Mike Deaver, deputy chief of staff. Deaver's name was on the list, which was almost equally divided among corporate executives, people from the news media, Hollywood personalities, and influential members of Congress and the administration.

A number of single guests were invited as individuals without escorts, including Georgetown hostess Evangeline Bruce, socialite Brooke Astor, CBS chairman William Paley, sculptor Louise Nevelson, and Washington cave-dweller "Oatsie" Charles. "Nancy -- I mean Mrs. Reagan -- rang me up last week and very kindly invited me," she said. "She thought it would cheer me up since Robert's in the hospital with a stroke for a second time."

The exception to the no-escort rule was entered on the guest list as "Mr. Arthur Mitchell & guest, actress Cicely Tyson." Mitchell is a co-director of the Dance Theatre of Harlem, which provided entertainment following the dinner, and he and Tyson appeared to be the only prominent blacks on the guest list.

Two nonpolitical organizations represented at the dinner were The Pilgrims of the United States and The English-Speaking Union, respectively the most exclusive and largest organizations dedicated to promoting Anglo-American relations.

Hugh Bullock, president of The Pilgrims, said the organization has "1,000 members and a 10-year waiting list."

"We are not nearly so exclusive," said John McCulloch, president of The English-Speaking Union. "We have 30,000 members and no waiting list."

From Congress, the president invited the Republican chairman of several important committees and ranking Democrats from the budget and finance committees.

Naturally, the Democrats were asked why they were there. "Well, we can help him," said Sen. Ernest Hollings (D-S.C.), a member of the budget committee.

In answer to the same question, Sen. Russell D. Long (D-La.) of the finance committee, and his wife, indulged in some joking. "We'd like to know too," said Carolyn Long.

"When the president invites you, you'd better be there, or fall out with your wife," the senator said. Guests at last night's dinner: President and Mrs. Reagan The Right Honorable Margaret Thatcher, M.P., prime minister of the United Kingdom of Great Britain and Northern Ireland, and Mr. Thatcher Miss Carol Thatcher, daughter of the prime minister The Right Honorable the Lord Carrington, KCMB,MC; secretary of state for foreign and commonwealth affairs, and Lady Carrington. s Sir Robert Armstrong, KCB, CVO; secretary of the cabinet Sir Michael Palliser, GCMG; permanent undersecretary of state, foreign and commonwealth office Sir Frank Cooper, KCB, CMG; permanent undersecretary of state, ministry of defense His Excellency the British Ambassador, and Lady Henderson Clive Whitmore, principal private secretary to the prime minister Julian L. Bullard, CMG; deputy undersecretary of state, foreign and commonwealth office Berard Ingham, press secretary to the prime minister Michael Alexander, private secretary to the prime minister Hon. Richard V. Allen, assistant to the president for national security affairs, and Mrs. Allen Hon. Leonore Annenberg, chief of protocol, and Hon. Walter H. Annenberg, former ambassador to Great Britain Hon. Anne Armstrong, former ambassador to Great Britain, and Mr. Tobin Armstrong Mrs. W. Vincent Astor, New York City Hon. James A. Baker III, chief of staff and assistant to the president, and Mrs. Baker Betty Beale, The Washington Star; Field Newspaper Syndicate Mrs. David K. E. Bruce, Washington, D.C. Hugh Bullock, chairman, Calvin Bullock Ltd.; president, The Pilgrims of the United States, NYC; and Mrs. Bullock Chief Justice Warren Burger, and Mrs. Burger Vice President George Bush, and Mrs. Bush Mrs. Robert H. Charles, Washington, D.C. Rep. Barber Conable Jr. (R-N.Y.), and Mrs. Conable Stanton R. Cook, publisher, The Chicago Tribune, and Mrs. Cook Justin W. Dart, chairman, Dart Industries Inc., Los Angeles Hon. Michael K. Deaver, deputy chief of staff and assistant to the president, and Mrs. Deaver Clifton C. Garvin Jr., chairman, Exxon Corporation, NYC, and Mrs. Garvin Secretary of State Alexander Haig, and Mrs. Haig Mr. Ralph Harris, Reuters, Washington, D.C. Sen. Mark O. Hatfield (R-Ore.), and Mrs. Hatfield Sen. Jesse Helms (R-N.C.), and Mrs. Helms Charlton Heston, Beverly Hills, Calif., and Mrs. Heston Sen. Ernest F. Hollings (D-S.C.), and Mrs. Hollings Bob Hope, North Hollywood, Calif., and Mrs. Hope Hon. Jeane Kirkpatrick, U.S. representative to the United Nations, and Dr. Evron Kirkpatrick Sen. Paul Laxalt (R-Nev.), and Mrs. Laxalt Sen. Russell B. Long (D-La.), and Mrs. Long John J. Louis Jr., chairman, Combined Communications Corporation, Northfield, Ill., and Mrs. Louis John I. B. McCulloch, president, English-Speaking Union of the United States, NYC, and Mrs. McCulloch Hon. Edwin Meese III, counselor to the president, and Mrs. Meese Arthur Mitchell, founder, Dance Theatre of Harlem, & guest, actress Cicely Tyson Robert Mosbacher, chairman, Mosbacher Production Company, Houston, Tex. Rupert Murdoch, publisher, The New York Post, and Mrs. Murdoch Enid Nemy, Society Editor, The New York Times Louise Nevelson, sculptor, NYC William S. Paley, chairman, CBS Inc. Secretary of the Treasury Donald Regan, and Mrs. Regan Attorney General William French Smith, and Mrs. Smith Roger L. Stevens, chairman, JFK Center for the Performing Arts, and Mrs. Stevens Hon. Walter J. Stoessel Jr., undersecretary of state for political affairs-designate, and Mrs. Stoessel Sen. Strom Thurmond (R-S.C.), and Mrs. Thurmond Hon. William E. Timmons, Timmons & Co. Inc., Washington, D.C., and Mrs. Timmons Hal Wallis, Los Angeles, Calif., and Mrs. Wallis Sen. Malcolm Wallop (R-Wyo.) Sen. John Warner (R-Va.) Secretary of Defense Caspar Weinberger, and Mrs. Weinberger Jack Wrather, Los Angeles, Calif., and Mrs. Wrather