From The Color Purple to School of Rock, Brits are conquering Broadway (except poor Keira Knightley)

It is sometimes hard to see past the feeding frenzy during the Christmas period of previews and openings on Broadway, but two shows in New York with strong British connections have created an exceptional buzz of anticipation and euphoria around Times Square.

First, there was Andrew Lloyd Webber opening School of Rock, his first show to premiere on Broadway since Jesus Christ Superstar in 1971, and in the same theatre, the gargantuan, gilded Winter Garden, where Cats frolicked across the Eighties and Nineties. And then there was the iconic – no other word, alas – musical version of Alice Walker's The Color Purple imported from our little Menier Chocolate Factory in Southwark, making an instant Broadway star of Cynthia Erivo, repeating her gut-wrenching, barnstorming performance, interrupted by two standing ovations during the show, alongside Jennifer (Dreamgirls) Hudson.

The Brits, as usual, are showing up well on Broadway, though it's hard to find anyone with a kind word to say about Keira Knightley in Helen Edmundson's Thérèse Raquin at Studio 54 ("Unnatural," said The New York Times). Two of the biggest current hits are Simon Stephens's The Curious Incident of the Dog in the Night-Time and Mike Bartlett's King Charles III, plays which originated at the National Theatre and the Almeida. Tim Pigott-Smith's definitive future King Charles is waving to the crowds directly across the street from Glee star Jonathan Groff's delightfully gormless King George III in the season's hip-hop sensation, Hamilton.

Added to which, Al Pacino is slaying them in the aisles in a new, so-so David Mamet play, China Doll. And the stand-out, sold-out hit of the season, Lin-Manuel Miranda's Hamilton, which even Lloyd Webber says has raised the bar irreversibly for the entire future history of the American musical, is prompting nightly queues round the block, and halfway along 8th Avenue, for a lucky dip $10 lottery ticket available to just 21 punters per show.

I imagine if you came from New York to spend a few days in the London theatre, and made the right choices, you'd have a similar reward. But there's always an add-on element of sizzle and adrenalin-rush on Broadway, even in low seasons, and that element was ratcheted up big-time by School of Rock, the latest kids' takeover show following the other two British imports of Billy Elliot (which faltered and failed) and Matilda (still running).

The 2003 School of Rock movie starred Jack Black as the rumpled, permanently hung-over wannabe bad-ass rock star, Dewey Finn, who sneaks a job as a stand-in teacher and moulds his 10- year-old charges into a heavy metal rock band before winning over their appalled teachers and parents.

In one of the more unexpected alliances in modern musical theatre, Lloyd Webber has had the book written by Julian Fellowes, not exactly Down-ton with the kids, and probably immune to the fact that Elgar is an anagram of lager; but he's done an efficient job, if not exactly discovering his inner rock god, while Lloyd Webber's riotously loud score (with lyrics by Glenn Slater, who did lyrics for the Phantom sequel Love Never Dies) incorporates both the film's songs and musical jokes into something sounding distinctly his own.

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Laurence Connor's production has exuberant Matilda-like choreography by JoAnn M Hunter, some brilliant 10-year-old rock musicians, cast from all over the country (where will we find their British equivalent when the show comes to the Palladium next year?), a lovely performance by Sierra Boggess as the teacher who melts at the sound of Stevie Nix on the jukebox; and, above all, a tremendously winning and energetic lead performance from unknown Alex Brightman as Dewey, channelling Jack Black but doing something gentler and even funnier all of his own.

The other new kid on the Broadway block, Cynthia Erivo, leads John Doyle's stripped and powerful revival of The Color Purple as the abused and suppressed Celie on a bare stage backed with floating chairs on a vertical floor of broken planks. We're in Georgia between 1909 and 1949. Black slavery in the Deep South, and in an African interlude, where Celie's estranged mother reports back on her missionary work, with a flurry of straw baskets and flowing tribal robes, is almost a metaphor in itself for domestic violence, sexual invasion and rivalry (Jennifer Hudson – delightful, if too young and sugary, is the sultry, seductive lounge singer Shug Avery; Nicola Hughes fitted the bill better at the Menier).

The songs of the 2005 musical – based on Walker's novel and Steven Spielberg's movie starring Whoopi Goldberg, who's one of the producers here – are a wonderful mélange of gospel, blues, jazz and ragtime written by a notable trio: Brenda Russell, whose dad was in the Inkspots; Allee Willis, a writer for Earth, Wind and Fire, and for Dusty Springfield; and one of Madonna's key collaborators, Stephen Bray.

They whistle up a storm of sound to match the storm of black freedom and liberation coursing through Celie's veins and rigidly defiant demeanour. When she explodes, the lid flies off and nearly the roof of the theatre, too. It's extraordinary to think that the show, and the story, still feels so needed in this day and age. And the black Broadway audience will be cheering it all the way.

In the foyer of the newly renamed Gerald Schoenfeld Theatre – Schoenfeld was a lawyer who took over the mighty Schubert Organisation in the early Seventies, along with another lawyer, Bernie B Jacobs, who has his own theatre right next door – there's a photo gallery of American titans. Al Pacino as the fictional Mickey Ross in China Doll hangs between George Soros and Warren Buffett. Ross is a financial mogul and political fixer holed up in a sleek apartment with his virtually silent assistant (Christopher Denham) trying to book a private plane to take his girlfriend from Toronto to London while fending off tax demands, uncooperative allies and potential criminal charges.

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You could see how Mamet in his pomp might have dramatised this crisis by at least populating the stage a bit more. Pacino's two-hour monologue, punctuated by a meaningless interval, is conducted as a one-way telephone conversation – through a suspicious-looking ear piece fixed on a wig that resembles a wet racoon in a high wind – with the girlfriend, his lawyer, the tax office, the plane-hire people; until a climactic, completely unprepared and frankly implausible catastrophe breaks the deadlock.

The audience don't seem to care. They love Pacino, as indeed do I when he's in the groove, which he is for a few short bursts of several minutes. But a lot of his acting here is an expert application of glue between thinking up the next line or speech, which may or may not be visible to him on several laptop screens and bits of paper scattered around the inertly beautiful setting.

Hamilton is a hip-hop, high-stakes, utterly original and intellectually challenging new musical about the Founding Fathers – not just Alexander Hamilton himself (intriguingly played and sung by the author) but also Thomas Jefferson, George Washington, James Madison and Hamilton's nemesis, Aaron Burr.

To have this narrative – running from the revolution of 1776 to the presidential election fight between Jefferson and Burr in 1800 – enacted by an all-black African and Hispanic cast is obviously cultural dynamite: the new country as a focus of assimilation and democratic politics, just as the brilliant hip-hop and rap score levels out into other more Broadway-friendly (and no less brilliant) musical modes as jazz, even a hint of Rodgers and Hammerstein.

The show's source is Ron Chernow's blockbuster biography of Hamilton published 10 years ago, the design a wooden edifice of planks, platforms and pulleys, part ship, part barn, a world of pioneering construction, costumes a mix of period frock coats, corsets and practical tights (it's all dead sexy, if you ask me) the performances in Thomas Kail's production, without exception, highly tuned and sprung like electric coils.

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Hamilton will sweep next year's Tony awards. This year's big winners, opening in the spring, were Fun Home, a drably dull, politically correct mini-musical at the Circle in the Square derived from Alison Bechdel's graphic novel, in which the gay, but unhappy, heroine deals with a seriously dysfunctional family (at three stages of her life) including her dad (Michael Cerveris in my week's second shocker of a wig), a funeral director who also comes out as gay and throws himself under a truck; and a breathtakingly beautiful staging of the 1951 MGM musical starring Gene Kelly and Leslie Caron, An American in Paris at the Palace.

The British and Irish talent in the latter, the best balletic dance musical since On Your Toes, includes director/choreographer Christopher Wheeldon, designer Bob Crowley – the designs are amazingly beautiful, perfectly dove-tailed with the projections of 59 Productions – and Royal Ballet star Leanne Cope, who has a Leslie Caron bob and an impish, high-wattage personality.

She partners Robert Fairchild, principal dancer with the NYC Ballet, in the Kelly role of Jerry Mulligan, the American GI who has just liberated Paris. Playwright Craig Lucas pushes the action back to 1945, with great results of added tension of "newness" after the war and an American expat composer, Adam Hochberg (Brandon Uranowitz), who guides us through the great Gershwin songbook while nursing a leg wound at the piano. After a theatre of war, a theatre of hope would engulf the Broadway musical for at least 15 years; until it had to start all over again in the Seventies.