Harry Hill’s latest musical traces Tony Blair’s bizarre career from student pacifist to war-mongering plaything of the United States. With co-writer Steve Brown, Hill has created a ramshackle, hasty-looking production that deliberately conceals the slickness and concentrated energy of its witty lyrics, superb visuals and terrific music.

The last thing it wants to seem is sophisticated and it starts off with a parade of New Labour grandees, all grotesquely overblown. John Prescott is a violent northern drunkard who wants to punch everyone in the face – including the Scots because ‘they’re too far north to be proper north’. Robin Cook is a cerebral sex maniac. David Blunkett gets pulled around by his guide dog because, being blind, he hasn’t fitted the lead correctly. Even John Smith’s fatal heart attack is mocked but the show avoids the charge of bad taste because it has a child-like innocence and a spirit of zany escapism.

Harry Hill could never be snide about anything and this show just wants to have fun. Princess Diana enters as a pouting bundle of guileless sexuality and Tony swiftly tries to seduce her until he’s halted by Cherie (an interesting rumour, but probably groundless). Tony himself is portrayed as an empty vessel, a clueless grinning drifter, whose quest for power is a substitute for his vanished hopes of rock-star fame. Cherie has been reimagined as a seductive black-clad chanteuse who ensnares her husband with a love song, ‘Ma Nom est Cherie’, (although ‘mon nom’ might have been better).

The show pulls together madcap humour from anywhere, and some of the sketches reveal strange shafts of truth. Saddam Hussein is portrayed as a New York stand-up with a stick-on moustache and a Groucho Marx cigar. Could Saddam be a Jewish comedian? Why not? Give it a go and see if it works. And it does, weirdly. In a cave in Afghanistan we meet Osama bin Laden who plots to destroy the West because he can’t master his envy of our hedonistic materialism.

The show ends on an exhilarating note as the cast unite in a satirical anthem denouncing despots and bad guys all over the world. Why, asks the song, do decent citizens always get lumbered with God-awful leaders? It feels joyously liberating. And it’s hard not to join in. This could be a smash.

Howard Brenton’s latest play is set in Athens in 399 BC. Socrates has been charged with denying the gods and corrupting the city’s youth and he meets his aristocratic friend, Euthyphro, outside the court. They instantly plunge into a debate about what is good and what is holy. Socrates wants to know if Zeus, who is clearly holy, performed a good deed when he raped Europa disguised as a bull. Euthyphro shushes him, anxiously. It’s bad form to call Zeus a rapist.

But Socrates couldn’t care less about public opinion. His life is a quest to discover the truth using reason and his ‘inner daemon’ as a guide. Brenton’s text subtly honours the rules of Athenian drama by locating the main events off-stage and letting witnesses tell the story at second hand. It’s a static and talky play. And all the better for it. The author captures the innocent quizzical character of Socrates and his method of reaching conclusions by laboriously analysing every possible angle of an argument. If you’ve ever wondered what it’s like to plough through the dialogues of Plato, you’ll find this an accurate and entertaining introduction.

Women scarcely feature in Plato’s writings and Brenton corrects this omission with comic scenes between an ageing courtesan, Aspasia, and Socrates’s young wife, Xanthippe. The rivals bicker over their conquests and Aspasia claims to have seduced Pericles in her youth. She boasts that she gave the great man all his best ideas, including democracy.

Jonathan Hyde’s Socrates is a charming bug-eyed vagabond in unshod feet and a moth-eaten toga. He’s blessed with an exceptional intellect and a Christ-like modesty but he’s bloody annoying too, like a clever child who pesters a tired parent with relentless questions. No wonder Athens got sick of him. He was charged with religious crimes because his enemies wanted him exiled but Socrates chose to drink hemlock rather than letting himself be spirited off abroad.

This theme of no-platforming is highly topical at the moment and its storyline sounds eerily familiar: a dishevelled and clownish visionary, versed in the masterpieces of Homer and Aeschylus, is brought low by a talentless mob of envious lightweights. It sounds like Boris and his noodle-brained MPs. He’d love to watch this play. Tom Littler directs with a keen eye for the big laughs, and his simple, elegant staging suits the compact space perfectly. The women’s robes are simply fabulous to look at. It’s rare to find a production that ends too soon. Some in the crowd wanted this play to last till midnight.