I'm curious what the BBC doc has to say about the Soviet lunar program; my impression (mostly from reading Asif Siddiqi's history Challenges to Apollo) is that the lack of political support and focus post-Gagarin lead to a late start on a lunar landing program, plus lack of funding and splitting resources between Korolev's N1-L3 architecture and Chelomei's programs. Between those factors, the uncertainty caused by Khrushchev's overthrow, and Korolev's death, it doesn't seem like the Soviets had much of a chance of beating the US to a lunar landing.