The two productions that have bookended Nicholas Hytner’s decade as artistic director of the National Theatre, Henry V and Othello, have much in common. There’s Shakespeare, Adrian Lester in the title roles and an ability to do that thing which Hytner has said National Theatre productions should strive for — holding up a mirror to the nation.

In 2003, that nation was at all-out war in Iraq. Today, it is still fighting, but now conflict in this modern (combat) dress production has the feel of attritional normality. And, although much of the action is set in Cyprus, Hytner still finds room for a whiff of English Defence League-style bigotry before we get there, when the senator Brabantio (William Chubb), backed by a couple of well turned-out thugs, confronts Othello for having sex with his daughter Desdemona. The crime, in the father’s eyes, is clearly compounded not only by the colour of Othello’s skin but also the otherness of his nation.

But it is a state of mind that should — and does — shape the foreground to this psychologically slippery play. Here, Hytner has cast his Hamlet Rory Kinnear as his Iago. That Hamlet production was most interesting for its ideas. It featured a police state, Denmark, and in one unforgettable moment it was suggested that Ophelia was murdered. Kinnear was a fine prince but the evening was much more interesting for its production than simply for Kinnear’s performance.

There is no such imbalance this time. The play is driven by an unstoppable, malign force in the form of Kinnear’s Iago. There are scenes in which he barely speaks and which you only belatedly notice the watchful, brooding figure with the thunderous stare in the corner of the room. When he does talk, there is no hint of duplicity in his breezy exchanges with the people he makes it his mission to destroy. The accent, though, is harder to get a handle on.

A cross between a Jewish taxi-driver and white South African, Kinnear may be going for a broad London, working class brogue that suggests an aspirational lower middle — or should that be upper lower — social class. At one point, he hilariously mimics Othello’s posh lieutenant Cassio (a dashing Jonathan Bailey) and later he clearly enjoys leading Roderigo — here terrifically played by Tom Robertson as an upper class twit — by the nose. Despite the ambiguity of that accent, I doubt there will be a Shakespeare production this year in which the language is better spoken and where the story is more clearly defined.

With most of the action taking place in Cyprus, Vicki Mortimer’s design appears to have been inspired by the cargo crate city of Camp Bastion, Britain’s military base in Afghanistan. The rooms are Lego-shaped boxes that serve as arrestingly banal mini stages to the action taking place within. Othello and Desdemona’s bedroom is not the usual boudoir bedecked with drapes in the Moorish style, but a space whose charmless interior serves as a starkly bland backdrop to the moment when Othello strangles his wife. And it is all the more convincing and harder to watch for that.

As Othello, the excellent Lester conveys a rare kind of urbane warlord. His descent into jealous rage appears rooted in a belief that there is more to life than giving orders and being professionally violent and that Olivia Vinall’s civilising and teasingly irreverent Desdemona is the way to find it. This is a man who is not just in love with his wife, but with the man into whom his wife has turned him.

We got a foretaste of Lester’s Othello when he played the Victorian black actor Ira Aldridge at the Tricycle’s recent production of Red Velvet.

But, actually, it is not so much Aldridge’s Othello that’s expanded upon here, as Lester’s Aldridge — a man whose sophistication and charm is a raft upon which he can rise out of the mire of white bigotry that surrounds him. Except, of course, Iago’s.