Armando Iannucci is well known for asking his actors to improvise their scenes around the script, and editing the best takes together. In one such improvised scene, James Gandolfini became angry enough to make Peter Capaldi drop out of character (he thought Gandolfini would "physically pummel me") and he asked the writers to provide him with a better come back.
Prior to filming, Armando Iannucci gained access to the US Department of State by flashing a simple photo ID to a security guard and saying "BBC. I'm here for the 12:30." He then spent a few hours walking around taking pictures for his set designers. The meeting in which General Miller is stood up by Linton Barwick was also scheduled for 12:30.
The shooting script after thirty days of filming was 237 pages long. The first cut of the film was 4.5 hours long. The final edit took four months to complete.
According to creator/director Armando Iannucci, the reason the UN vote is so abrupt is that they didn't have enough money to recreate the Security Council of the UN.
Many scenes set at 10 Downing Street (the Prime Minister of the United Kingdoms's office) were filmed at the real 10 Downing Street. The production gained access to the location largely because the staff were extremely excited to meet the actors who were playing their fictional counterparts.