Four letters are emblazoned above a colonnade, which overlooks a statue of a lion sinking its teeth into the flank of a horse. 'SPQR': Senatus Populusque Romanus - The Senate and the People of Rome. It's a simple stage, but one which immediately sets out the essential background for a tragedy unfolding in the last years of the Roman Republic. The senate rules on behalf of the people, not over them, and the mighty victories of Rome's generals, which have brought pride and prosperity to the citizens, are commemorated in statuary. This tension between the republican ideal and the lure of the charismatic military leader has already brought the city's major political players to breaking point.

One of Shakespeare's less convoluted plots, Julius Caesar is a simple tragedy with complex undertones, where treachery is punished but subtlety of motive is acknowledged. Fresh from a resounding victory over his erstwhile ally Pompey, Caesar has been awarded ever greater powers and looks set to become Rome's sole ruler. In a city which prides itself on rejecting monarchical tyranny, this causes great anxiety among the political classes, while the wider population is content to bask in collective victory without fear of the broader consequences. Motivated variously by fear, patriotism, pride, republican zeal, spite and ambition, a group of conspirators set about neutralising the would-be tyrant. Whose side should we really be on? Is Caesar a wronged hero or a dangerous populist with tyrannical ambitions? Are the conspirators treacherous ingrates or self-sacrificing patriots? This is a production that does a terrific job of showing how difficult – and fascinating – the debate can be.

The title role is fabulously played by Andrew Woodall. His Caesar is delicately balanced. He is statesmanlike, his speech elegant but powerful, his vocal delivery exquisite; he is dignified and poised – but his dismissive pride is so unmistakeable that self-regard narrowly avoids tipping into self-parody. It's very effective, and it's easy to imagine how an individual who appears so impressive from a distance might be failing to retain the admiration and loyalty of those closest to him.

The conspirators play their parts with a contrasting naturalism, with offhand delivery and lots of casual gestures. It's a bit distracting but actually very successful in making them seem artless and fervent, and in inviting us to sympathise with their struggle. This does mean that Brutus (Alex Waldmann) arguably lacks the authority and presence to justify Mark Antony's praise 'This was the noblest Roman of them all', but he is otherwise strong, plausibly principled and conflicted, so I think they get away with it.

James Corrigan brings power and pathos to the role of Antony. His motives seem particularly cynical in this production, which I felt detracted a little from the power of his famous eulogy, but it's certainly a fair reading of the text. Martin Hutson's highly-strung Cassius, desperate rather than petulant, was impressive, and Hannah Morrish created a nuanced and affecting Portia.

It's been said before that the second half of Julius Caesar struggles to make an impact in the wake of the first. After a heady start of political machinations, beautiful oration, rabble rousing, murder and riots, it's hard work for the audience, and presumably the actors, to be plunged into a mire of off-stage battles and on-stage suicides. The uncomfortable argument between Brutus and Cassius, however, as they sit in the ashes of their grand intentions, is a fist-chewingly juicy display of post-conspiratorial guilt and hysterical bonding, and the small but crucial part of Octavius is skilfully played by Jon Tarcy with a patrician air and a marvellous marriage of overweening schoolboy and burgeoning commander.

From a modern political point of view the whole thing seems very sad. We're shown that demagoguery can carry the day over rationality and principle; we're bewildered by violence and confused by the interplay between warring factions, and the whole thing is a tragic foreshadowing of tyranny to come – the conspirators, whatever the merits of their intentions, are trying to stave off the inevitable, as within a few short years the self-governing populace will indeed come under the control of a single dictator, their hard-won privileges lost for centuries to come. Tragedy indeed.