Barack Obama and David Cameron have been meeting to discuss policies affecting the US and UK. President Obama said the countries’ alliance is key to providing global security.
The US President also met Nick Clegg and Chancellor George Osborne.
The President and the Prime Minister are expected to attend a barbecue hosted by their wives for the families of military personnel involved overseas.
Barack Obama spent most of Tuesday at Buckingham Palace where the Queen hosted a special banquet.
Guests included Gordon Brown, Tony Blair and Sir John Major along with Hollywood stars Tom Hanks and Kevin Spacey.
The US leader used the event to highlight the unique bonds that his homeland shares with Britain.
Read more: The war on terror special report
He told the guests at the white-tie dinner: “As we approach the 10th anniversary of 9/11 I’m particular grateful for the solidarity that the United Kingdom has shown to America over the past decade.
“From that day to this you have been our closest partner in the struggle to protect our people from terrorism attacks and violent extremism from around the world despite very heavy sacrifices here.
“And allow me to pay tribute to the contributions of your military forces who have stood shoulder to shoulder with us for decades.”
The Queen paid tribute to the US and said the country remains “our most important ally”.
She added: “But our relationship goes far beyond our military and diplomatic ties. In your inaugural address, you spoke to the American people of the values that lay at the heart of your nation’s success: ‘honesty and hard work, courage and fair play, tolerance and curiosity, loyalty and patriotism’; and of the ‘sturdy alliances and enduring convictions’ with which your nation had met past challenges and would meet future ones, too.
“If I may say so, these values underscore much of the life of the United Kingdom also.
“Together with our alliance, they continue to guide our actions as we confront the challenges of a changing world.
“It is unfortunate that there are so many troubles facing the world today, but we are encouraged that in most respects our two countries see these problems in the same light.”
Michelle Obama will highlight the importance of education on a trip to Oxford University where will once again meet pupils from the all-girl Elizabeth Garrett Anderson School (EGA).
Mrs Obama first met pupils from the north London secondary school when she accompanied Barack Obama on their visit to London in April 2009.
She made a surprise trip to the school, where she urged the young women to “be the best that you can be” and to have “confidence and fortitude” to determine their own success.
Around 35 EGA pupils are due to take part in a day-long “immersion experience” at Oxford, including campus tours, career discussions and mentoring sessions, before meeting Mrs Obama.