Making a committee meeting into drama is less like making poetry out of the telephone directory than it might seem. Michael Heseltine does not storm out of the government every week, but we have all been in some pretty tense meetings in our time. Away days and weekend think-tanks at mediocre hotels have even greater potential for excitement and intrigue, given the opportunities offered by alcohol and neighbouring bedrooms. Normally, everyone shiftily returns to work on the Monday, agrees how useful it was to have such a clear exchange of views, praises the value of blue-skies thinking (as it is now called) and quietly agrees to forget the whole thing.

The meeting of 15 Nazi officials at a mansion in Wannsee, in the suburbs of Berlin, on Tuesday 20 January 1942, broke most of the rules of these affairs. For one thing, the food was excellent. No one stormed out. Tempers were restored almost as soon as they had been lost. And this time, although the minutes were buried, the session greenlighted a plan that changed history, and humanity's understanding of itself, for ever. This was the away day that rubber-stamped the extermination of six million Jews.

Under the direction of Frank Pierson, Conspiracy (25 January, 9pm, BBC2), a BBC/Home Box Office film for TV shown in the States last May, did everything it could to underplay the inherent melodrama, knowing that the less histrionic the re-enactment, the greater and more sinister would be the contrast with the meeting's consequences. As a result, the dialogue was as legalistic as a law report and as nuanced as in a Jane Austen adaptation. Death was wreathed in politic euphemisms, so that "evacuation" became the solution to a "storage problem" with "these Jews". When the verb "to kill" slipped out, the stenographer stopped typing, because no one wanted to supply ammunition to treacherous future historians. To give Reinhard Heydrich (the SS general who convened it) his due, this was one of the best-chaired meetings in history. Whenever voices were raised, he recommended a break for food or drink. At the end of the terrible day, the "Final Solution" got a unanimous vote of confidence.

The script, by Loring Mandel - based, to what degree we were not told, on the sole surviving record of the meeting - did not attempt to get inside the Nazi mind. It simply looked on and gawked. Racial slurs, often salaciously sexual, were permitted around the table. The only really interesting speech on the Jewish race came from Wilhelm Stuckart, a relative moderate who opposed mass extermination. He maintained that, far from being a "subspecies", the Jews were "sublimely clever". But if it failed as an explanation of evil, Conspiracy succeeded in connecting us to the mind of the bureaucrat, and to the pschodynamics of the meetings he obsessively holds.

The moral problems inherent in dramatising anything to do with the Holocaust grow when a dramatisation is as good as this. Conspiracy could not have been more seriously untitillating in intent, but it was still entertaining, and that in itself is unseemly. The sumptuousness of the food and the opulence of the mansion were deliberately sick-making, but you risked retching on the feast of character acting: Stanley Tucci (of Murder One and Big Night), with his tense, sotto voce portrayal of Adolf Eichmann; Colin Firth as Stuckart, persuading us first that he was on the side of the angels, and then that he was still (although he obviously was not), by his own lights, a moral man; David Threlfall as Dr Friedrich Kritzinger, a civilian in a blue lounge suit who believed he was morally superior to the barbarians around him, but who exemplified Yeats's line about the best lacking all conviction.

Then there was the problem of Kenneth Branagh as Heydrich. With his fair hair and sleek haircut, he looked unlike himself, and denied himself any histrionics. Yet Branagh's thin-lipped acting was still the sort that steals scenes, even at its most self-effacing. It seems that Heydrich used a similar mechanism to control the meeting and get his way. Yet the build-up to his late, flashy entrance (he comes by plane) had an extra-textual consequence. The viewer hung on for the arrival of The Star, an Orson Welles or Laurence Olivier or Marlon Brando, and the level of anticipation did Branagh no favours. There is generally something troubling and self-serving about Branagh's acting; I felt that a couple of weeks ago, watching Shackleton (Channel 4). Perhaps he should abjure parts for leading men for a while. Yet the film would have fallen apart without his star turn. He deserved the Emmy he won for it. Perhaps the irritation he inspires served him well this time.

When the meeting finally broke up, the camera escaped the claustrophobia of the house for the driveway, where, in the bracing outdoors, the chauffeurs and bodyguards of the men who participated in the meeting were having a snowball fight. We had earned the respite of physical humour, but the eternally disciplined Eichmann was furious and slapped his adjutant across the face. "Sorry, sir, it just happened," he said. "Not in uniform. Nothing just happens," Eichmann replied. Nor does it, but Conspiracy showed how, even to the participants, it can sometimes feel like that.

Andrew Billen is a staff writer on the London Evening Standard