After leaving the Royal Marines in 1947, Wheeler joined the BBC, initially as a sub-editor at the Latin American division of the World Service. Wheeler's long career as a foreign correspondent began with a three-year posting to Berlin in 1950, partly thanks to his fluency in German. He returned to the UK and became a producer on the fledgling current affairs series "Panorama" in 1956. As part of "Panorama"'s team, he travelled to Hungary to cover what would become known as the Hungarian Uprising. Taking "Panorama's" camera into the country, despite being told not to, he filmed the jubilant Hungarian reaction to the rebellion. He and the Panorama producer (and his then wife) Catherine Freeman had to persuade the BBC to give the story prominence. Just hours after Wheeler returned to Britain, Russia re-entered Hungary and crushed the revolt.