President Obama will outline in a speech Wednesday how much the world has changed since the U.S.-British partnership emerged victorious from World War II, but also argue that the relationship remains the cornerstone of global security.

The theme, outlined by administration officials here Tuesday, is part celebration of the military partnership, which has waged war in three Muslim nations over the past decade, and part reassurance that the heavy cost has been essential.

Obama will deliver the address, characterized by advisers as “the anchor speech” of his six-day European trip, to the British Parliament at Westminster Hall, becoming the first American leader to do so in that historic venue.

But his argument, directed at the European public, will be politically challenging. Britain and several other European members of NATO are sharply cutting back spending and public services to rebalance budgets strained by the weak global economy — something the United States hasn’t done to the same extent.

In making his case to a war-weary Europe, Obama will describe the U.S.-European partnership as one that goes beyond a military alliance, declaring that shared political values are helping inspire the rising demand for democracies in the Arab world.

“He’ll speak to the fact that we’ve obviously come through a very difficult decade, but in some respects we’re turning a corner,” Ben Rhodes, a U.S. deputy national security adviser, told reporters.

Obama came to office promising to reinvigorate the various U.S. alliances with Europe, which the previous administration divided into “old Europe” and the newer democracies of Central and Eastern Europe that more fully supported U.S. counterterrorism policies.

But his attention to strengthening U.S. ties to other parts of the world, particularly Asia, worried some European leaders, who thought he was taking the relationship for granted. His swing through four nations this week is, in part, an effort to dispel those misgivings.

While still popular with the European public, Obama has left some European leaders struggling to understand an administration that, in the case of Libya, has been willing to cede leadership to NATO.

“People in Europe misperceived him as a global president, a Dali Obama come to save the world,” said Constanze Stelzenmueller, a transatlantic fellow with the German Marshall Fund in Berlin. “Now they know differently, but they still like him, and he commands great respect and popularity in Europe. But for the policy elites, the picture is quite different.”

His address at Westminster Hall will be the most substantive event of the trip so far after a start heavy with ceremony.

On Tuesday, Queen Elizabeth II welcomed Obama and the first lady, Michelle Obama, for his first state visit here. The official greeting took place just before noon at Buckingham Palace.

The Obamas walked up the red carpet to the palace door, where the queen, her ubiquitous handbag in the crook of her arm, greeted them with a handshake and smile. Prince Philip stood by her side.

The first couple gave the queen a handmade, leather-bound album containing original photographs of the June 1939 visit to the United States of her parents, King George VI and consort Elizabeth, known more recently as the queen mother.

Inside the palace, the Obamas also met with Prince William and his new wife, Princess Catherine, the Duke and Duchess of Cambridge, who tried to keep a low profile to avoid distracting from the visit. In honor of their recent wedding, the Obamas donated six MacBook computers to the Northern Ireland chapter of PeacePlayers International, a nonprofit organization on the royal couple’s wedding registry.

Afterward, as the Obamas watched from a palace terrace, a military band played the national anthems. Cannons sounded a 41-gun salute, and Obama, with Prince Philip, inspected the Scots Guards.

Waiting outside the palace, hairdresser Joan Lewis, 52, said she wanted a glimpse of Obama “because this is part of my black history, and I’m very proud of him.”

“There isn’t any airs or graces about him,” she said.

Many lined the streets and gathered outside the Obamas’ tour sites on a warm and clear afternoon.

The Obamas visited Westminster Abbey and laid a wreath at a tomb, surrounded by poppies, in memory of “the unknown warrior.” Obama wrote in the guest book, “It is a great privilege to commemorate our common heritage and common sacrifice,” but added the wrong date, “24 May 2008.”

Obama also paid a courtesy call at 10 Downing St. to see Prime Minister David Cameron, with whom he will hold more extensive meetings Wednesday.

The leaders made an unannounced visit to the Globe Academy, a math and performing arts school with a high percentage of poor children.

About a dozen students showed the men their design projects, and when someone suggested an investor might want to finance one of them, Obama had a reference at hand. “Donald Trump?” he asked. “I have a connection to him.”

The two men then shucked their jackets and played table tennis with the kids.

The evening ended with a state dinner at Buckingham Palace, where Obama, in white tie and tails, toasted the alliance as “a commitment that speaks to who we are.”

Staff writers Anthony Faiola and Karla Adam contributed to this report.