Popular music and politics have shared a long, often turbulent history. “From Strange Fruit,” the anti-lynching song made famous by Billie Holiday, the civil rights hymn “We Shall Overcome,” to the Specials‘ hit “Free Nelson Mandela,” musicians have frequently proved irksome to governments by drawing attention to uncomfortable issues of the day. Two new documentaries, “Dixie Chicks: Shut Up and Sing” and “The US. vs John Lennon,” cast light on this combustible relationship. Hannah Patterson reports on the docs playing at the London Film Festival currently underway.