The TV presenter, 53, and Graham, 39, separated "a number of weeks ago", according to her agent.
"It's sad for both of them but Carol felt it has naturally run its course as relationships sometimes do," her spokesperson said.
He continued: "She decided that it would be best to bring it to an end as amicably as possible, so they separated a number of weeks ago."
Carol's appearance on Saturday is her first public outing since she broke the news to The Mirror.
The former Countdown co-host looked stunning in a tight-fitting grey dress, which she accessoried with a matching bag and nude heels.
She topped off her look with light grey gloves and a cosy winter jacket, which kept her warm during the day.
Carol and Graham, who were last pictured together at the Lord of the Dance: Dangerous Games gala night on 3 September, got together in 2012 after meeting through Carol's fundraising work for the RAF.
The TV star has previously been married twice. In 1985 she married Royal Navy office Christopher Mather but they divorced the following year.
She then went on to marry Paddy King in 1990 and had two children together. The couple divorced in 2000.