When The Incredibles came out in 2004 who could have known how prescient it was? Amid the wonderful Pixar animation, charming characterisation and rambunctious wit, its plot gave a comic glimpse of a core theme of the Marvel and DC franchises just around the corner – namely that society isn’t convinced that it wants superheroes at all.

Rather than get all po-faced about it, as most of those other films do, Bird had his tongue firmly in cheek. And now the writer and director is at it again, both celebrating and mocking his Sixties superheroes in a sequel that is even more fun than his original. To coin Bird’s own cheery shorthand for his gifted protagonists, this family film is simply ‘super’.

The plot picks up where it left off 14 years ago. Superheroes are still illegal, but the Parr family – Bob/Mr Incredible, Helen/Elastigirl and their kids – just can’t help themselves, and are in hot pursuit of the Underminer, a small man with a big drill as he attempts to rob a city bank from below ground.

The trouble is that Mr Incredible (voiced by Craig T Nelson) is more brawn than brains. And by the time he’s failed to save the bank or catch the crook, Metroville’s city centre has been demolished – not unlike New York, Gotham or Metropolis whenever superheroes choose to intervene.

“Would you prefer we didn’t help?” Bob asks the cops. “Well yes!” the definitive answer he didn’t expect.

The Parrs are homeless, broke and facing a gloomy future of regular employment, when billionaire fan Winston Deaver offers another solution – campaign to reverse the superhero prohibition by giving the public and politicians an insider view of what it takes to fight crime.

To that end, Deaver’s techie sister Evelyn designs miniature cameras for the superhero suits. There’s one catch: Bob is too much of an insurance risk; they want the less destructive and more media-friendly Elastigirl (Holly Hunter) to be their advocate for superhero rehabilitation.

Once Bob’s dealt with his male pride and a new life minding the kids, Helen is let out of the box to fight crime solo – and is so brilliant that she might just change public opinion. If only her new-found benefactors could be trusted.

The film is a treat on every level. The retro-futuristic aesthetic is gorgeously realised, in everything from clothing to house design to Elastigirl’s sleek new motorcycle, and in action sequences involving a runaway train, a helicopter chase and a hijacked luxury yacht. There’s atmosphere (Elastigirl’s nocturnal pursuit of the new villain, Screenslaver), family melodrama (teenager Violet Parr’s attempts at school romance are ruined by her superhero identity), topical themes (Screenslaver’s reasonable disagreement with society’s over-dependence on technology) and enormous amounts of humour.

Much of the comedy is derived from Bob’s domestic travails, exacerbated by the emergence of his youngest boy’s abundant superpowers; it’s difficult to keep your kid in a cot when he can travel through dimensions, or allow him to play with animals when laser beams come out of his excited eyes.

That aspect of the story becomes even more delicious when Bob turns to an unlikely babysitter, in the form of the superhero costume designer Edna Mode (voiced by Bird himself), who looks a little like the infamous James Bond assassin Rosa Klebb and takes an instant shine to her tiny new client. Samuel L Jackson again voices the Parr’s friend Lucius Best, aka Frozone – who’s cool in every sense of the word. But new additions to the superhero world are more eccentric. As one, Reflux, introduces himself: “Medical condition or super power: you decide.”