There is a particular kind of political documentary that tries to put us “in the room”, to tell us how historic decisions were made and how the fallible humans who made them felt. But on 11 September 2001, when planes hijacked by al-Qaida terrorists destroyed the twin towers of New York’s World Trade Center and took the lives of nearly 3,000 Americans, the chaos was such that there was no single “room”. President George W Bush and his advisers, afraid for their own safety and constantly searching for information, were on the move all day and had to conduct their business in airbase bunkers, the back room of a school and aboard the president’s jet, Air Force One.

Nevertheless, 9/11: Inside the President’s War Room (BBC One) gives the sensation of being in the room in a way that few documentaries ever have. That day has often been described as a disaster movie no screenwriter would dare imagine. Here, it is a horrifyingly tragic but also propulsive story, with twin narratives following the president’s movements and the developing carnage on the ground, minute by minute.

The film’s archive footage has plenty of Adam Curtis moments, such as Bush killing a fly on the Oval Office desk, seconds before giving the gravest speech of his life, to underline that every moment of 11 September had something odd or terrifying in it. But as every relevant government official shares their recollections on camera, the vivid pictures are outstripped by personal anecdotes. We hear from the situation room captain, who recalls having to brace herself against the president’s desk as Air Force One made a steep emergency takeoff – “I went partially weightless. I was petrified” – and the deputy communications director, who got flustered when Bush’s doctor handed out anti-anthrax pills and took his whole week’s ration in one hit.

Chiefly, though, this is an insight into the mind of the star interviewee: George W Bush. At first, we see his notorious folksy simplicity, apparent in his eerily counterintuitive decision to ignore, for several long minutes, the news about the second tower being hit, for fear of being impolite to a class of Florida seven-year-olds having a presidential visit. Bush also called for those around him to stop and pray, more than once, while still in the eye of a storm of unknown lethality and proportion. “Prayer can be very comforting,” he says here.

Such reactions could be read as bizarre in the face of doom, or natural responses to a situation where what could immediately be achieved was unclear. One interviewee says that, while analyses of Churchill or Roosevelt in wartime look at actions that took weeks to complete, Bush on 9/11 is a study of a leader being forced to make epic choices on the hop.

This is where Inside the President’s War Room is most revealing. We hear how anger became the strongest of Bush’s conflicting emotions: fear and sorrow and a determination to safeguard US citizens had to make room for the desire to, in Bush’s words, “kick their ass”, before it was known whose ass or how. By that evening, the president had publicly formulated the “Bush doctrine”, which said harbouring terrorists was to be treated as the equivalent of perpetrating terror. A new American pathology, the “war on terror”, was born in haste.

The consequences of this are clear from the fact that this documentary, marking 20 years since 9/11, airs just as the ensuing military intervention in Afghanistan concludes. The thought of that war and, moreover, the US and its allies’ 2003 attack on Iraq, hangs over the whole piece, making the simplest emotional moments complex. The politician expressing the helpless horror of seeing the twin towers fall on TV is Karl Rove. The bowed head, overcome by the emotion of remembering the dilemma over whether or not to shoot down United Flight 93, belongs to Dick Cheney.

Are those moments still affecting, knowing that those men went on to wreak horrors of their own? Yes, but to its credit, Inside the President’s War Room makes sure that context is explicit. Being in the room doesn’t stop us looking beyond.