Hull Truck Theatre has begun its celebration of Hull as UK City of Culture with a splendid joint production with the Royal Shakespeare Company which ticks all the boxes. The Hypocrite combines zanily comical farce with a respectful nod to a key moment in Hull's and England's history.

In 1642, with England on the brink of Civil War, Sir John Hotham, appointed Governor of Hull, refused the King admission to the city: there is an element of truth in Hullensians' claim that they started the Civil War. Hotham, however, was no hero and over the following months he changed sides regularly with the fortunes of war. In the end he was executed by order of Parliament; had the Royalists' cause triumphed, he would probably have been executed by them.

Richard Bean pays serious attention to "the world turned upside down". His play begins at the end, with Hotham's execution; ballad singers punctuate the action with punkish protest songs by Grant Olding; at the end, after the cast have pursued their own comically uncivil wars, they gather together for a paean to parliamentary democracy.

But in between, the evening justifies Bean's observation that the events in Hull in 1642-43 were farcical. He condenses 14 months into three days, a crazy succession of new arrivals, new problems, constant knocks on the door and people hiding in the coal cellar. Poor Sir John has other problems, too: a quarrelsome and unfaithful wife, a love-sick daughter, a chronic lack of money and many other potential disasters.

Director Phillip Breen gets vivid performances from all in his 20-strong cast. Mark Addy is perfectly cast as the principle-free Sir John, oddly likeable and switching easily from bombastic dignity to deflating asides, savouring Bean's clever word-play. He and Caroline Quentin, his aggressive and openly contemptuous wife, make the most of as inventive a set of insults as you'll find anywhere.

Jordan Metcalfe and Rowan Polonski are a delightfully camp double act as the Duke of York and Prince Rupert; Sarah Middleton, the Shakespeare-reading daughter desperate for romance, careers about like Ophelia on speed; Pierro Niel-Meo's rational, law-loving Durand Hotham has a touching innocence; Laura Elsworthy makes Connie, the servant, the only sensible person there. The striking performances continue throughout the cast, with a special mention for Danielle Bird, the "ancient" servant, knocked down, tied up, confined in multiple articles of furniture, and still tumbling and trapezing.

Max Jones' set is elegant and functional, his costumes as inventive as the text and direction, and every trick and illusion is carried off with panache.

Perhaps in some ways the production is a bit much. Do we need so many characters, so many twists, such a long evening? In practical terms, the stage is sometimes so full that key entrances are masked. But excess goes with riotous invention – and there's plenty of that!

The Hypocrite runs at Hull Truck Theatre until 25 March, and then at The Swan, Stratford-Upon-Avon from 31 March to 29 April.

Read our ten highlight of Hull's City of Culture