The dinner was being held at the British embassy in Washington, and came amid a whirlwind of events for Clinton's last week as America's top diplomat.
After four years on the job, she will say a final goodbye to the State Department on Friday, handing the baton to Senator John Kerry who is due to be confirmed by Senate later in the week.
Clinton's husband, former president Bill Clinton, and her designated successor, Kerry, were among the guests sitting down to the dinner, which also included her daughter, Chelsea, and son-in-law Marc Mezvinsky.
Other top names who were invited to join the evening included long-time Senate colleagues, senators John McCain and Dianne Feinstein; outgoing Defense Secretary Leon Panetta; and US ambassador to the United Nations, Susan Rice.
The chairman of the US Joint Chiefs, General Martin Dempsey; IMF chief Christine Lagarde; as well as treasury secretary designate Jack Lew and designer Oscar de la Renta were also on the guest list provided by the British embassy.
Hague said that in facing up to the challenges ahead "the alliance between the United Kingdom and the United States and our other allies will remain of fundamental importance."
"I think international affairs will be more difficult over the next 20 years. We face a huge challenge of terrorism. Particularly after 9/11," Hague told CNN television.
Clinton has traveled almost a million miles, visiting 112 countries, in her four years in office. But her globe-trotting was abruptly cut short in December when she caught a stomach bug, which caused her to faint and hit her head.
Her doctors subsequently discovered that after the concussion she had developed a blood clot in a vein in her head, behind her right ear, and ordered her not to fly for some time.
Hague on Monday joined the chorus of praise for Clinton's achievements as secretary of state, in an opinion piece for the Huffington Post in which he set out plans to seek G8 action against rape as a weapon of war.
Britain will chair the Group of Eight richest nations this year, and Hague said he would make it a "personal priority... to secure new international action against the use of rape and sexual violence as a weapon of war."
"In the crowded field of Secretary Clinton's achievements her work on women's rights is particularly inspirational. In this as in so many of the challenges of our time, Britain and the United States are natural allies," he wrote.
Although Hillary Clinton would be absent from the G8 meetings, having left office, "her legacy will be part of the foundations we build on, and US support will be essential if we are to tackle this problem," Hague wrote.