Glenda Jackson is the queen of Broadway in a hit-and-miss King Lear

There's fame. And then there's global celebrity. On the night I went to see Glenda Jackson as King Lear in New York, even the massive "round" she received the moment she arrived on stage was as nothing compared with the pre-curtain applause granted to Hillary Clinton, former senator of the Big Apple and defeated presidential candidate.

You could see why one legend would want to see another legend in the theatre – especially since Sam Gold's production of Lear sets the tragedy in Miriam Buether's design of a gilded room which might just be a reference to the glitter and gaudiness of Trump Tower. It also emphasises its political resonance in the most heavy-handed way, with Ruth Wilson's Fool pulling up her trousers to reveal stars and stripes socks at the end of a rant about Albion's politics.

The performances are big and occasionally wonky

Almost everything about the production is heavy-handed, in fact. I'd admired Gold's direction of Annie Baker's plays but none of that sensitivity or warm humanity is on display here. Everything is obvious and laid on with a trowel from Goneril's explicit coupling with Edmund (all sexual fluids and no knickers), to the original Philip Glass score which is played by a string quartet who insistently underline the action, sometimes even standing centre stage in the most distracting manner.

The performances are big and occasionally wonky, with Aisling O'Sullivan as Regan and Elizabeth Marvel as Goneril shouting their lines in different accents (did they grow up continents apart?), and Jayne Houdyshell's gender switched Gloucester mumbling while making no mark at all. Since the only directorial concept seems to be to throw in everything including the kitchen sink, the performers who thrive best are those who seem to understand the words and play them pretty straight: Pedro Pascal is a nicely sneering Edmund, John Douglas Thompson an affecting, straightforward Kent. The deaf actor Russell Harvard is a ferocious Cornwall (with his part signed by Michael Arden) though I couldn't for the life of me decide why he was wearing a kilt. (Ann Roth's costumes are irritatingly random, making the entire thing resemble a comic operetta.)

Jackson is without doubt the best thing on the stage

The evening, it has to be said, is never dull and amidst the whirling mess, there are anchors. Wilson making a good fist of the doubling of Cordelia and the Fool is definitely one of them. She has such charisma that she battles her way through. The storm scene – played in front of a golden metal front curtain – was peculiar (characters have to open a door to emerge and have no space to move) but emotionally effective; there's a moment where Wilson sinks to her knees in frozen despair at her master's mad raging. She seems to unravel in front of your eyes and she and Douglas Thompson display a quiet compassion which is a welcome breath of air in such a loud production.

Which brings us to the great woman herself. Jackson is without doubt the best thing on the stage, finding her own line through the chaos, with that magnificent voice swooping supplely on the words and turning them every way she wants. It is quite astonishing that at the age of 82, after a 25-year break, she is not only playing Lear but giving us a second interpretation of the part, quite different from the one she offered at the Old Vic nearly three years ago.

How lucky we are to have her back on stage

That version moved me more; it had a wounded humanity and gentleness that the American portrayal lacks. But this is nevertheless a thing of wonder, centring on Lear's fear of madness and his sudden realisation that it was office not an ingrained authority that has given him power. Jackson, arriving in evening dress, gives a little sigh before giving up her kingdom, and then sits back to enjoy herself, as if it was all a parlour game. Her rage when it all goes wrong is carefully charted.

I found myself thinking of her peer, Ian McKellen, also a notable recent Lear, as the performance progressed. She shares his ability to turn on a sixpence, to segue into towering anger from nowhere, to command absolute clarity from the language. It's also a very physical reading: this Lear seems to shrink as misfortune brings him low, and Jackson finds profound tenderness and sorrow in lines such as "I have ta'en too little care of this", when she is confronted by poverty and distress. But she never loses her regal bearing; even in the scene where a mad Lear confronts a blind Gloucester, she is imperious as she presents her hand to be kissed.

Watching her, I thought how lucky we are to have her back on stage, and what we have been deprived of by her years in politics. She has no regrets. I do. If only she had played all the great roles she was destined to play. But this late renaissance is in itself a blessing.