From the White House, via the pool report:
On the occasion of the Official Visit, The President and Mrs. Obama gave the Prime Minister and Mrs. Cameron a one-of-a-kind Braten 1000 Series Grill hand made by Engelbrecht Grills and Cookers of Paxton, Illinois. Symbolizing the personal friendship between the President and Mrs. Obama and Prime Minister and Mrs. Cameron, the gift commemorates their May 2011 visit to 10 Downing Street where together they grilled and served food to American and British Armed Service Members.
An American classic, the wood and charcoal burning grill is customized with American and British friendship flags engraved into the utility shelf and a personalized plaque mounted on the exterior lid. The grill and all its component parts are made in the United States and Engelbrecht Grills and Cookers has been praised for its environmentally friendly practices. The gift also includes two White House chef jackets each featuring American and British flags, and the Great Seal. Prime Minister and Mrs. Cameron's names are embroidered onto the front of their individual jack
The grill, presumably, looks a little like this, from Engelbrecht's website:
The non-custom version can be purchased for $1,895.