But Bonham Carter said last year that the couple may not work professionally again, as her husband was "getting sick" of her. Although clearly a joke, those light-hearted words were taken by some present as a hint about their personal relationship.
Later that month, a spokesman for Bonham Carter dismissed as "just nonsense" suggestions that Burton had cheated on her, after the director was pictured with a mystery blonde woman at a cinema in Hampstead, north London.
A photo of Burton embracing the woman showed nothing more than "a goodbye peck on the cheek", the spokesman said at the time.
The couple have been guests of Prime Minister David Cameron at his country retreat, Chequers.
They live, or lived, in a series of three conjoined houses, one decorated to each of their tastes and a third home for their children - son, Billy, 11 and a daughter, Nell - and live-in nanny.