Hamilton was hailed as revolutionary theatre in 2015, with its rapping 18th-century statesmen, its funky, feelgood hip-hop and a cast predominantly comprising actors of colour. It went on to conquer Broadway and West End audiences. How does that original Broadway staging fare on the flat screen, streamed by Disney+ in the midst of lockdown?

It spoke to the moment then, and it speaks to us now, say director Thomas Kail and Lin-Manuel Miranda, the creator and star, in their short, socially distanced preamble to this highly anticipated film of the show. “We are all thinking about what it means to be American,” they add. Even if these words are not in direct reference to the America of the past few weeks, with its upsurge of anti-racist protest, their story of the Caribbean-born immigrant hero and founding father of the US, Alexander Hamilton, speaks to us obliquely of all that remains neglected in America’s history while shifting the parameters at the same time.

Its rousing opening scenes remind us of that great American ideal of equality and speaks of slavery and civil rights in the 18th century. “I never thought I’d live past 20. Where I come from, some get half as many,” sings Hamilton at the start, and his words echo the dangerous fate that awaits so many of America’s black or immigrant underclass now, as debate around Black Lives Matter protests has highlighted.

Even more remarkably, it keeps all the power of a live performance while simultaneously adding a filmic pizzazz including some breathtaking aerial shots. There is extraordinary direction – again under Kail – so that the cameras capture the mise en scène of theatre without losing any of the closeup intimacy of film.

Miranda’s lead performance brims with understated brilliance. Every actor alongside him performs with just as much conviction though some with more swagger: Phillipa Soo is a demure Eliza Hamilton until she breaks out, gloriously, into beat-boxing; Daveed Diggs is a funny, scrappy Thomas Jefferson with his edgy raps and his attitude; Renée Elise Goldsberry is a heartfelt Angelica Schuyler, with a sensational, and soulful, singing voice to boot.

The film keeps all the energy of the stage, from the large-scale war scenes to the political power battles which are staged as rap battles. But it also takes us into tight shots of Angelica as she sings of her secret love for Hamilton, or of King George (Jonathan Groff), the camera so close we can see the spittle of his anger over the loss of his American colony.

There are profanities and urban speak, but it never sounds brash or uncouth, and the period costume (breeches for men, Gone With the Wind style dresses for women) has an edge of modernity to it. All its radicalism comes wrapped in fantastically infectious songs, stirringly delivered, and the lack of book is no hindrance to the complications in its plot.

“It takes on a different meaning when you see black and brown performers telling the origin story of our country,” says Miranda, and he is right in that these performers remind us of the contribution of immigrants like Hamilton to American history. But more than this, it is the intelligence in the lyrics, and the clever subversions of the “period drama” form that make this such a joyous musical to watch.

It has political intrigue, personal tragedy, a sex scandal and lightning changes of mood that sweep us along at speed. Best of all is the wit that sits neatly alongside its politics: “Immigrants, we get the job done”, says one character archly, and the audience laughs knowingly.

“What is a legacy?” says Hamilton, in the heart-stopping last moments, and the film leaves us reflecting on America’s.

• Hamilton is available from 3 July on Disney+