The Britain's Got Talent duo played tracks from their debut album Together, before helping turn on the station's Christmas tree lights.
Jonathan & Charlotte also performed a rendition of 'Holy Night' and told the crowd that they had sung the carol as a twosome for the first time just hours before the gig.
"I've never experienced anything quite like it," Jonathan said. "One lady was crying in the audience and she later told me it was because our song had been played at her mother's funeral. It was quite emotional."
Charlotte added: "I've never been so cold in my life but it was worth it to see so many people stop and listen to us sing. It's now officially Christmas!"
The pair also told the crowd of their upcoming UK tour, which begins at the Rhyl Pavilion on June 22 and concludes at London's Hammersmith Apollo on June 29.
Watch Jonathan & Charlotte perform 'Il Mondo È Nostro' on The Alan Titchmarsh Show below: