Why have the Brits done so well in this year's Tony Award nominations?

Judging by yesterday's Tony nominations, it won't be long before Donald Trump declares a trade war on Theatreland. British actors, writers, designers and directors were so dominant across the non-musical categories at New York's major theatre awards that the Philistine-in-Chief might reasonably start harrumphing about the drama deficit between Broadway and the West End. Sure, we've exchanged Hamilton for Harry Potter – fair and square – but beyond those two blockbuster behemoths, the scales are fundamentally tipped in the West End's favour. What better way to rectify that than a Rylance Tax?

It looks a remarkable haul – more Brits, I believe, than ever before. A bevy of best actors – Andrew Garfield, Tom Hollander, Mark Rylance and Jamie Parker – should outflank Denzel Washington, while the great Glenda Jackson is hot favourite for best actress. Some of our finest stage stalwarts are up for the featured roles. Any category containing Noma Dumezweni, Denise Gough, Deborah Findlay and Susan Brown (with a side order of Laurie Metcalf) is enough to set one salivating, and it's a real pleasure to see Anthony Boyle, Hogwarts' star pupil, in the running to add a Tony to his mantelpiece. Hat tips, too, to Harry Hadden-Paton and Diana Rigg on the musical side.

Brits have all but taken over the direction, set design, lighting, sound and costume categories on the drama front

America's long been taken by British actors. The astonishing thing, this year, is the influx of creatives: Brits have all but taken over the direction, set design, lighting, sound and costume categories on the drama front. Both Marianne Elliott and lighting designer Paule Constable could take home their third Tonys; Mark Rylance too. Sound designers Gareth Fry and Adam Cork are gunning for their second, as are Harry Potter's John Tiffany, Neil Austin and Steven Hoggett. All of them, incidentally, cut their teeth – and, indeed, continue to do so – in Britain's subsidised theatres; a mark of what arts funding makes possible.

True, the British boom is partly a result of a slight Broadway season – one of the reasons so many shows racked up 10 or more nominations. Even so, when the National's staging of Angels in America becomes the most-nominated straight play in Tony history, something's going good guns. Given it's effectively America's national play, its soar-away success looks like selling coals to Newcastle.

One of the marvels of the Tony haul is how speedily London shows have swept across to New York

There's a reason I keep talking in terms of trade. There's one set of names you won't see up for these gongs – the producers. Arguably, their prize comes at the box office, but they're behind all the rest. Because British theatre has, in recent years, established a wealth of connections in New York. A concerted effort has truly come off.

One of the marvels of the Tony haul is how speedily London shows have swept across to New York: Harry Potter made the jump much faster than Hamilton, but Angels and Travesties are only just out of the West End. Beyond Broadway, there have been other successes: Yerma bedded in beautifully at the Park Armoury, after the Old Vic's Hairy Ape; Martin McDonagh's Hangmen was a hit, as was People, Places and Things.

The Menier Chocolate Factory has long linked up with American producers, but the Royal Court, Donmar Warehouse and the two Vics, Young and Old, are now regularly ensuring extended lives overseas for their biggest hits. The Royal Shakespeare Company has a longstanding relationship with BAM, and the National even has its own New York office. Over in the commercial sector, ATG has brought its first Broadway theatre, while it's not just Harry Potter but also Mean Girls (which she co-produced) that has cemented Sonia Friedman's status – already strong – as a major player.

What's fascinating is that New York transfers are being built in from the start

It shows no sign of stopping, either. The Ferryman heads over in a few months, after a post-West End break, and only on Monday, two more transatlantic transfers were announced: James Graham's Ink is off to the Samuel J Friedman Theatre and Dennis Kelly's Girls and Boys is heading to the Minetta Lane Theatre. There are more to come. Matthew Warchus has confirmed that Girl From the North Country will head to Broadway – deals are being discussed – and I'd be astonished if The Inheritance wasn't eyeing up its chances given its setting, Stephen Daldry and an Anglo-American cast. What's fascinating is that such options are being built in from the start. I've got it on good authority that one of this summer's biggest openings (go on, guess) has already established its path to New York.

All of which is great for audiences at home – not just because Broadway box office offsets straightened arts funding, but because those connections bring interesting work this way. We're seeing more American playwrights on British stages than ever, while the subsidized sector is scooping up idiosyncratic hits and supporting them here – witness Fun Home at the Young Vic and Hadestown at the NT.

The Tony Awards might honour individual achievement – and we shouldn't take anything away from those crossing their fingers until June 10 – but beneath the surface, the scale of this year's British success is as systemic as it is seismic.