If you had to summarise the difference between British and American attitudes to the Second World War, you could just say that while America was making Saving Private Ryan, Britain was rerunning Dad's Army. This is not a case of American bombast versus British modesty. If anything, the myth of war is even more deeply embedded in the British psyche than in the American. It is just that we are so certain we saved civilisation that we can afford to make jokes about it. America, at least in that aeon between the Vietnam war and 11 September 2001, has been so nervous about whether it has used its superpowers for good that it needs to talk to itself sternly from time to time. Americans must remind themselves that, once upon a time, brave men moved among them.

Tom Hanks and Steven Spielberg, the star and the director of Saving Private Ryan, must feel it is already time for a refresher course in self-esteem. Having cost $120m, Band of Brothers (Fridays, 8.30pm, BBC2) is an expensive reiteration of their film's message of wartime heroism, and the British viewer has to jump a few hurdles before he can really begin to enjoy this ten-part dramatisation of a US paratroop company's progress through Europe from D-Day to the capture of Berchtesgaden.

While our chests may burst with pride that it was filmed in Hatfield and that its two leading actors are British, this is a drama-documentary that reduces the British contribution to a cameo. The first episode of the opening double bill featured just one Englishman, and he spoke broader mockney than Jamie Oliver (he even said: "Yeah, it's pukka, innit?"). We may feel uneasy, too, at all the assertions of courage, particularly when the interviewees who begin each episode are edited to provide no explanation as to why they were so keen to risk their necks for Europe. It will not do for Band of Brothers to follow Easy Company into a concentration camp in the penultimate episode and stamp it "Why We Fight" (although that is what it does) - they were wearing out boot leather at army camp long before they heard the word "Holocaust".

But once you stop quibbling, you start feeling. After two outings, you know what it's like to be parachuted into France one summer night in 1944, how it is to see comrades shot dead or hang lifelessly from a tree, hoist by their own parachutes. Band of Brothers lets us in on the deep gloom before the invasion - in one telling scene, the company is not watching a Cary Grant film on the eve of D-Day - and the muddle and panic afterwards. Its craftsmanship is astounding.

Spielberg found a new visual style for war. Here, as in Saving Private Ryan, the hand-held camera-work, sometimes as jerky as a silent film, implies that we are getting a grunt's-eye view. The colours are neither black and white nor Technicolor. The technical term is, apparently, desaturated, "how viewers might expect footage from that period to look" - although, in fact, we know from Carlton's The Second World War in Colour that the real colours are much more garish. The artistry is not merely visual, either. This series employed 10,000 extras and scripted lines for around 500 actors. Next to it, Laurence Olivier's big-screen Henry V ("band of brothers" comes from Hal's battle speeches) is a school theatrical. Yet Band of Brothers is also an intimate drama about the qualities of leadership. In episode one, we are drawn in by the psychological flaws of the ghastly sadist Lieutenant Sobel. In episode two, in contrast, we appreciate the right stuff within Dick Winters, the man who takes command in France. But Winters, a non-drinker who abhors violence, is a mystery himself, and one we'll keep watching in order to solve.

Saving Private Ryan, after its amazingly visceral opening, turned into a conventional war film that bowed to the plot. What the various directors and writers of this series have done is use the style pioneered by Spielberg to tell a real story factually, in as much of its sprawling complication as possible. When a man dies and that man is named, we can be sure a man of that name truly did die in those circumstances. Damian Lewis as Winters and Dexter Fletcher as Martin had the real Winters and Martin as the ultimate judges of their performances - although the BBC production notes do not relate whether Herbert Sobel survived to offer his verdict on David Schwimmer's brilliant impersonation of an incompetent sociopath. It is not just great drama. It is great history.

Spielberg has defended the BBC's decision not to show Band of Brothers first on BBC1: "We tried like hell not to make it mainstream." But he overemphasises the difficulties of the narrative - there's swooshing music, fantastic visual effects and cool one-liners in each episode - and under- estimates his audience's patience. Having paid £7m into what HBO generously calls a BBC co-production, the corporation should be selling it to as many licence-fee payers as possible. That the camouflaged young men of the 82nd Airborne Division currently deployed in the deserts bordering Afghanistan look remarkably like the fictionalised 101st Airborne Division of 1944 makes the series even more relevant. It's the "event television" we are always being promised. In brave times, Lorraine Heggessey, BBC1's controller, has displayed a pitiful lack of courage.

Andrew Billen is a staff writer on the London Evening Standard