There’s a simple-minded glee about racial stereotypes in Richard Bean’s England People Very Nice in the Olivier – the first of the new season (the seventh) of Travelex £10 tickets productions -- that threatens to engulf the audience in despair and disbelief, but Nicholas Hytner’s inventive and fast-moving production just about keeps the evening afloat.

And you can rationalise the cartoon caricature side of things in the fact that the cast is a crowd of detainees in an immigration centre putting on their own play about the waves of incoming nationalities over the years, starting with a comic book representation of Romans bopping cavemen over the head with clubs to the trite accompaniment of a live folk group.

This sequence sets the visual tone of Mark Thompson’s design as a mix of extraordinary lighting tricks, paint book graphics, projections and animations (supervised by Pete Bishop and lighting designer Neil Austin) which suggest a mixture of Asterix, 1066 And All That and Joan Littlewood’s Theatre Workshop at its fag-end and crudest.

The Romans are succeeded by the Huguenots, the Irish and the Jews in a carefree caper with repeated patterns of resentment at new arrivals filtered through the recurring love affair of Sacha Dhawan and the wonderful Michelle Terry in various guises. There’s feedback, too, on the grotesquely exaggerated sounding board of the Bethnal Green pub where Sophie Stanton’s hilarious, raucous barmaid greets each new mob with a cheery expletive, a joke with a good pay off when she is similarly disgusted by the absence of the Americans during the Blitz.

The other pub regulars are Fred Ridgeway’s chirpy Cockney philosopher and Trevor Laird’s passive Jamaican, prophesying “rivers of blood” from the start and finally withdrawing “home” to Barbados. But the second act stills the laughter as it comes up to date with the journey of Dhawan’s Bangladeshi Mushi – who invents the nation’s favourite dish, chicken tikka masala -- through the minefield of the National Front, Muslim bovver boys in Brick Lane and the blind fundamentalist imam with two hooked hands who demands one of Mushi’s twins as a religious saviour.

Bean the playwright usurps Bean the glib pamphleteer in these latter scenes of street violence, gentrification (celebrating “an eclectic mix” in Clerkenwell) and the resolution of the barmaid’s personal life and political prejudice. The very high level of acting extends to Elliot Levey’s clutch of fanatics, Tony Jayawardena’s blind imam, Olivia Colman’s earnest director (“We took a democratic vote to close all discussion on the script”) and Aaron Neil’s imposing chief rabbi and svelte Bangladeshi bigwig.

-Michael Coveney