Barack Obama ended his first state visit to Britain Wednesday with his attendance at a farewell dinner hosted by Queen Elizabeth II, during which the president once again stressed the "special and essential" ties between the two allies.

Indeed, the two words have dominated British newspaper headlines since Obama and Prime Minister David Cameron first used them in their co-written article published on the Tuesday edition of The Times.

"Ours is not just a special relationship, it is an essential relationship -- for us and for the world," they wrote.

Again, at their joint press conference after 90 minutes of closed-door talks Wednesday, Cameron said Britain's relationship with the United States is a "living working partnership" that is "essential to security and prosperity."

Obama described the bilateral relationship as "one of the oldest and strongest alliances the world has even known" in his speech to both Houses of Parliament at Westminster Hall Wednesday, which is regarded as a rare treatment for a foreign head of state and was previously accorded only to a handful of eminent figures besides British monarchs, including Nelson Mandela, Charles de Gaulle and the Pope.

To demonstrate the special relations, the Obamas were invited to stay at Buckingham Palace, an honor only given to two other U.S. presidents during the past century, and only another U.S. president since the Queen took throne.

But the first day of the visit was mainly pomp and ceremonies, as the Queen welcomed the Obamas and showed them around at the royal residence. The essential part started Wednesday as Obama had a meeting with Cameron and addressed hundreds of British lawmakers.

Topics at the bilateral talks included global economy, terrorism, Afghanistan, Middle East and North Africa.

The two leaders agreed that the death of Osama bin Laden "marks the most significant blow against al Qaida since its inception," they also vowed continue the "mission" in Afghanistan.Both renewed calls for Libyan leader Muammar Gaddafi to step down.

"specific areas" were also identified for bilateral cooperation in the coming months, including security and support for armed forces personnel, collaboration in science, higher education, volunteerism and international development, and the development of cyberspace.

In addition, the two sides agreed to work together to promote economic growth, prevent conflict in "fragile states," improve global health particularly for girls and women, and mitigate the effects of climate change.

Obama was scheduled to leave here early Thursday for France for the G8 Summit.