The words ‘iconic’ and ‘legend’ are so bastardised, especially when talking about music (when people really mean ‘enduring’ or ‘good’, or ‘popular’ or ‘old’), that they’re pretty much empty and really annoying.

But in Hyde Park, under a rose-tinted sky sliding into twilight, as those eight foreboding notes which presage ‘A Forest’ reverberate from the stage, this delayed-drop intro truly is iconic. There is no other pop song like it: the chills it gives on a sweltering day (over 30 degrees in central London) have shivered the spines of hundreds of thousands of teenagers all over the world. And 65,000 of those teenagers, some of us now in our fifth, sixth or seventh decades, are gathered here on pilgrimage for The Cure’s 40th anniversary gig.

It’s an extraordinary setting, the stage wrapped around by gargantuan screens and flanked by two massive Ent-ish trees, all of which will be used to dazzling effect, particularly later as the night goes darker still. And the visuals more than live up to what you expect from this band: enchanting, magical, witty, clever and strange. Tim Pope, director of memorable 1980s videos for The Cure, is here wearing a T-shirt that says: “Yes, I am filming it. No, I don’t know when you’ll see it. Don’t even ask.”

With a bill including Roger Waters, Eric Clapton and Paul Simon the Barclaycard BST Summertime series of gigs is an unabashed classic rock retro-fest. But among many things The Cure demonstrate tonight is that they are not nostalgia-tripping their way to the bank. Do not mistake them for a ‘heritage act’ – yes, they are our musical DNA, architects of British post-punk-into-pop, but their currency, relevance and influence echoes elsewhere in today’s line-up, not least The Twilight Sad and Interpol.

The members of The Cure love this band and its songs as much as we do

A life-long Cure fan (like any sensible 1980s teenager I had the hugest crush on Simon Gallup and Robert Smith interviews were plastered on my wall) of course I knew I would enjoy the gig. But, foolish me, I wasn’t quite prepared for the dazzling proficiency of a band not wallowing in past glories but stunningly shit-hot, seriously at the very top of their game, the sound quality is tremendous and every note and word played perfectly with freshness, vibrancy, joy, energy, ferocity and above all an immense amount of love. The members of The Cure love this band and its songs as much as we do, they play with the same intensity of love and passion with which we have cherished their music for the last four decades.

Robert Smith’s cute, small smile out-beams the relentless sun and his animated delivery of every lyric illuminates the night. Later, when he leaves the stage at the end of the gig with his hand on his heart and a promise to “see you again very soon” – joshing “it’s been a good first four decades, here’s to the next one. HA!” – he is clearly brimful of emotion.

British Summer Time Festival - London
Matt Crossick/PA Wire/PA Images

Gallup’s skip-hop moves propel him all over the stage, while he carries that low-slung heroic bass god pose with unspeakable coolness (and the pink bass is especially delicious). The two of them grin at each other frequently through the set, and Simon’s pulling rock-riffage with guitarist Reeves Gabrels and rocking out alongside keyboard player Roger O’Donnell and drummer Jason Cooper. There’s an extraordinary tiny moment at one point during ‘Burn’ when Smith and Gallup are playing back to back, Robert cranes his head in to Simon’s shoulder in an almost feline motion that looks heartbreakingly sweet. Maybe he was telling him a dirty joke.

And the set-list! What a 40th birthday gift! Delight, surprise, unadulterated purest joy! Really this is just picking out faves (full set-list below) but tonight ‘A Night Like This’ (my unequivocal top-of-the-list ‘pleeeease do it!’ song) is shatteringly majestic; the compact poetic beauty of ‘Lovesong’ is pure charm; ‘Burn’, with those searing, aching riffs is sublime in every sense; and ‘A Forest’ is incomparable, that iconic, unique, atmospheric, unlikeliest of anthems. The gigantic shiny pop of ‘In Between Days’, ‘Friday I’m In Love’, ‘Why Can’t I Be You?’ are obviously perfect in a massive outdoor arena like this; the chillier works (‘Disintegration’, ‘Play for Today’, ‘Push’) somehow sit perfectly comfortably alongside them. A deftly curated setlist, devised by a man who knows his fans.

This may be a 40th anniversary celebration but this is The Cure, so there could never be grandiose self-congratulatory pomposity to it. Smith may be demanding and a perfectionist, but he is also a wry, witty performer, his expressions and moves ones we’ve shadowed for decades. He really is, as this gig proves, a godlike pop genius whose music has united souls around the globe. But he’s also this bloke from Crawley with a sly sense of humour and a naughty glint in his eye.

“Of course 40 years ago this weekend it was the first time we played as The Cure, in The Rocket in Crawley. If any of you had asked me then what will you be doing in 40 years’ time, I think I would have been wrong in my answer,” Smith says before the set’s gloriously punked-up finale. “It’s thanks to everyone around me that I’m still here. This last bunch of songs is for everyone that’s still here, who came on the journey.”

That last blast of raw early tracks – ‘Jumping Someone Else’s Train’, ‘Grinding Halt’, ’10:15 Saturday Night’ and ‘Killing An Arab’ (what a way to finish!) – brought the diehards and hardcore fans to the front. With the brilliant bunch of blokes from Norway and the divine London Irish contingent The Big Issue pogoed (quite politely) and moshed (fairly mildly) and literally everybody in that park felt 40 years young.

The Cure: heroes and legends. And a completely fucking amazing live band.

Set-list:

Plainsong

Pictures of You

High

A Night Like This

The Walk

The End of the World

Lovesong

Push

In Between Days

Just Like Heaven

If Only Tonight We Could Sleep

Play for Today

A Forest

Shake Dog Shake

Burn

Fascination Street

Never Enough

From the Edge of the Deep Green Sea

Disintegration

Encore:

Lullaby

The Caterpillar

Friday I’m in Love

Close to Me

Why Can’t I Be You?

Boys Don’t Cry

Jumping Someone Else’s Train

Grinding Halt

10:15 Saturday Night

Killing an Arab

Image: Matt Crossick/PA Archive/PA Images