Every schoolboy knows - or used to know - two "facts" about King George III: he was mad as a hatter and once mistook a oak tree for the King of Prussia.

Until doing a spot of research in preparation for Alan Bennett's The Madness of George III at the National's Lyttelton Theatre, I'm ashamed to admit that this remained almost the sum total of my knowledge about the sad monarch. But by the end of this fine play there can't have been anyone in the audience who hadn't come to care deeply about this remote historical figure.

Like Bennett's television series Talking heads, it is a piece that combines humour with deeply affecting compassion. In less sensitive hands one could imagine the play becoming a distasteful spectacle in which the audience, like 17th-century visitors to Bedlam, are invited to laugh at lunacy. Bennett, however, with the help of an outstanding performance from Nigel Hawthorne, turns the king into a figure who is both loveable and tragic, and the audience sympathises with him on every stage of his journey through madness.

The play concentrates on the king's first serious illness in 1788-89, which prompted the Regency crisis. With great skill, he sets the human suffering of the king against its political consequences, with the Whigs rallying around the Prince of Wales in the expectation that he would soon assume power. At its most basic level, the play offers an informative and entertaining history lesson.

But it is the treatment of the king in the hands of his doctors that lingers most powerfully in the memory. Dosed with purges and emetics, bound to a restraining chair, blistered with hot glasses and gagged. George III's suffering is a terrible spectacle to behold. This is not a play for the squeamish. There is a pungent scatological content, not only in the doctors' fascination with the king's bowel movements, but also in the deranged compulsive monologues of the king himself.

But thanks to Nigel Hawthorne's performance, we always view the king with pity rather than distaste. From his first entrance he suggests the essentially benign nature of his faintly absurd character, and hi stammers and spasms of agony as the illness takes its grip are achieved with almost unbearable verisimilitude.

The great tragedy about george III was that his affliction was essentially physical rather than mental - a painful metabolic disorder called porphyria - and Hawthorne heartbreakingly suggests a man trapped inside his own illness, unable to communicate its nature to those making such cruel and clumsy attempts to cure him.

Nicholas Hytner's production has one or two longueurs, but it skilfully balances the play's public and private concerns, and there are a whole host of fine supporting performances, most notably from Julian Wadham as the cold and contained Prime Minister, William Pitt, Charles Kay as the most sinister of the doctors, and Janet Dale as the king's ugly but beloved wife.

The play movingly evokes King Lear, but as George III slowly recovers it takes on an almost celebratory atmosphere. After so much that has been harrowing, there is a final flourish of comedy yet the laughter is tinged with sadness. As Bennett reminds us at the end, the king's madness was to return.