It was a hectic day that began in Paris, paused in Rome and ended outside of London, and when President and Mrs. Reagan got to bed tonight, it was in Windsor Castle.

The Reagans checked into the 800-year-old official residence of Queen Elizabeth II a half hour late today, but a spokesman for the queen assured American reporters that since she is something of a world traveler herself she understands how one can get behind schedule.

In a slight breach of British protocol, the president kept making his wife precede him in situations where he should have been first. And while the British public is looking askance at the gaffe, the royal couple seemed to handle it all gracefully. A couple of times Prince Phillip tried to encourage the president to step forward and take his place by the queen. In the end, the Reagans and their host and hostess reached a compromise and all walked in line together toward the castle's entrance, where Knights of Windsor waited to welcome them.

Later, presidential press secretary Larry Speakes told reporters he thought that in the president's mind it was "a question of ladies first, a fine old Reagan family custom."

Prince Phillip and Prince Charles wore the customary morning suits that they put on for visiting heads of state, but President Reagan wore the same dark blue business suit he had worn all day for his visit in Rome with the pope, the president of Italy and the prime minister.

The queen wore a yellow silk suit with a straw hat to match. And Nancy Reagan's beige dress was her third costume change of the day. She had worn a black-and-white print dress from Paris to Rome early in the day, then changed into the traditional long black dress with black mantilla for the audience with the pope and afterwards changed into the two-piece beige dress she wore to Windsor. By the time she reached the castle she had added a straw hat. She changed yet a fourth time tonight for a formal dinner party Queen Elizabeth gave, but the White House did not have details about the gown.

The Reagans flew from Heathrow Airport by helicopter to Windsor Castle and got an aerial view of one of the places the queen calls home. After the welcome, the queen took the Reagans on a tour of the sunken gardens in the terrace and then on through an archway at the end of the State Apartments to the Quadrangle in the castle's Upper Ward. As the first U.S. president since Woodrow Wilson to be a house guest at Windsor, Reagan was obviously somewhat overwhelmed.

After that, though out of view, the Reagans were scheduled to present their "suite" to the queen, according to James Rosebush, deputy assistant to the president and Mrs. Reagan's chief of staff.

The "suite" means the people accompanying the president, who in this case are Secretary of State Alexander Haig and his wife, Pat; White House Chief of Staff James Baker; National Security Adviser William Clark and his wife Joan; and Deputy Chief of Staff Michael Deaver and his wife, Carolyn. They're all staying at the castle, too. After the presentation the queen actually escorts her guests to their room. The queen's quarters are just "down the hall," said Rosebush.

The Reagans are staying in the Lancaster Tower, which has a main bedroom, a smaller bedroom, two dressing rooms, two bathrooms and a sitting room. Rosebush could not remember any of the colors in the apartment, which he saw in May on one of two trips to advance the Reagans' 10-day journey, but others said the main bedroom is yellow and the ladies' dressing room is blue and white. The sitting room is done in cream, brown and pink. In the dressing room there is a collection of miniatures and in the main bedroom portraits of the royal family's ancestors.

Rosebush described the apartment as "impressive but not pretentious." He said he did not remember it as being as "grand as Versailles" but thought it was very comfortable and wouldn't mind staying there himself sometime.

He described the magnificent view from the windows that look down a long walk in Windsor Great Park where the president will ride Tuesday morning with Queen Elizabeth.

He said then that a White House telephone was installed in the Reagan suite, a custom when the president travels.

Another spokesman for the president said it is "standard procedure" for the White House to take food and water for the president on foreign trips.

"But I'm sure he'll be eating what they do at Windsor Castle," said spokesman Pete Roussel.

United Press International reported that Buckingham Palace had told the president he couldn't bring along the food taster who usually travels with him.

Last night at the dinner the royal couple gave for the Reagans the guests included the Queen Mother, Princess Anne and Capt. Mark Phillips, Prince Charles and Lady Diana. A palace spokesman said it would be the only occasion when Diana joined the Reagans during their two-day visit in Britain. She is expecting a baby in two or three weeks and will not attend a state banquet the queen will give in honor of the Reagans Tuesday night.

Others among the 38 guests at tonight's dinner were U.S. Ambassador to Great Britain John Lewis and British Amabassador to the United States Sir Nicholas Henderson. They dined on fillet of haddock, breast of chicken stuffed with mango and a pancake filled with raspberry jam and whipped cream.

In Rome, Mrs. Reagan visited a drug rehabilitation program where more than 85 youths waited an hour and a half to talk with her. Accompanying Mrs. Reagan was Ruth Rabb, wife of U.S. Ambassador to Italy Maxwell Rabb. The first lady listened to personal testimonials about drug abuse. Later, as she was about to leave, she commended the youths' determination to solve their drug problems. She delighted them when she said in Italian "Te amo" (I love you).