Photograph courtesy of Dave Hogan

Yes, I cried. Everybody cried. When one person stopped, another would set them off again, and you ended up with a parkload of weeping punters. Then Carole King cried and set us all off again. Half the people I know were there, it turns out, and they all cried, then said it was one of the greatest nights of their life. It was a watershed concert, if only for the cascade of tears running off to lower ground (in this case, Wellington Arch). Carole King hadn't played in London for 27 years. The flood defences may be better now but the audience, I would bet, is more susceptible.

I cried at 'Home Again', four songs in, and I did well to make it that far. I held out longer than most. Home. Again. I cried for a vanished family household where Tapestry turned on the record deck more weeks than not. Everybody cried, for love and loss and passing time, tears brought up from the well of memory. There's no point pretending otherwise. I don't think it sentimental or indulgent to emphasise that this happened. I think it would be a misleading omission not to. Tapestry is locked into that many lives, in that remarkable way.

Has any album ever achieved so fully what it set out to do as Tapestry? To weave and sing a life, that is, one that turns out to be everyone's life. The lives of portly polo-shirted men not all that much younger than its creator. ("This is what 74 looks like," says King, who was young and old when she made the record and is now old and young as she performs it. And by God, if that's what 74 looks like, should I get to 74, I'd take it like a shot. Minus the sequins. Maybe.) The lives of women who are now the age King was in 1971, when Tapestry was released. The life of me, the same age as the record, give or take. All of us will be singing it on the walk out when the show is over.

The greatness of Tapestry emerges in layers. There are the original songs themselves, each an extraordinary encapsulation of its particular theme. Another record – a relationship album – might have opened with 'I Feel The Earth Move' (the overwhelming rush of joy and desire that marks the start of love), placed 'So Far Away' (separation, loneliness, drifting apart) somewhere in the middle, and concluded with 'It's Too Late' (sorrowful yet honest recognition of the end). Tapestry gets that over with three songs in and keeps moving, because it's not a relationship album. It's a life, woven and sung. It says so on the tin: "My life has been a tapestry..." Then there is the effect of time upon songs about time and of change upon songs about change. These layers have taken 45 years to accrete. The scale varies from song to song and layer to layer; the acuteness of focus on the small moments, the great, blurry sweep of life blowing by. And now, here we are, and Carole King is 74 and singing our lives, and everybody's crying, including Carole King.

Who is, let's get down to brass tacks, one hell of a performer. I mean, yeah, emblematic of the singer-songwriter movement and all that, but to concentrate on the singer part for a moment, damn, can she sing. She's got the power and the rasp; she can make it move; she can make it swing; she can make it catch you there. A lot of showbiz know-how went into Tapestry along with a lot of soul, and every bit of both is out there tonight. I have no wish to slight her daughter, Louise Goffin, also a singer-songwriter, who plays a significant role in the night's events. Yet when the two duet – including on 'Where You Lead', which King, uneasy at its original woman-devotedly-following-man theme, is at pains to recast in a mother-daughter dynamic – the difference between an honest-to-god trouper, which Carole King is, and a person who sings, usually, simply because the songs are hers, could not be more apparent.

Nobody so exactly represents the evolution of mainstream American pop from '60s teen bubblegum to '70s singer-songwriter introspection because nobody else ever stood at the pinnacle of both. In person and in her craft, Carole King grew up with the art form. What is even more astonishing is that she somehow managed to sum up each with the same song. Her co-written 'Will You Love Me Tomorrow' as recorded by The Shirelles in 1960 is the perfect expression of the teenage girl's fear of succumbing to sweet talk that disappears the next day, along with the seducer. King's own version, released on Tapestry 11 years later, is the perfect expression of the fear that haunts, however dimly, every adult relationship – that love will flicker and die, as it does. The same audience that instinctively understood the one went on to know all too well about the other. Carole King was there for them, each time.

The second part of the show stresses her earlier career, with only one number – the exultant, soaring 'Jazzman' – post-dating Tapestry. The rest are hits she wrote for others with Gerry Goffin, several compressed into a medley ('Take Good Care Of My Baby', 'It Might As Well Rain Until September', 'I'm Into Something Good'), although she lavishes particular time and care on a tender version of a relatively obscure Freddie Scott song, 'Hey Girl'. Perhaps she feels, rightly, it deserves more notice.

If we pan out further – beyond Tapestry's place in the canon and in pop's chronology; beyond its connection to our own lives, young and old and in-between – another view presents itself. You often hear it said of artists such as King (I heard it several times on the night) that there won't be others like them. It's true. There won't. That's not because pop music is worse than it was; far from it, although the mainstream will surely never again support work and careers like King's. It's because a type of American music integral to the American Century seems to have run its course. Again, that is not to say American music is over – such grand statements invariably fall foul of the evidence, as fascinating new music piles up to refute them. But the supremacy, the simultaneous artistic and commercial triumph, of this particular kind of American pop, of great popular innovations from the rock side of the aisle, the kind so exactly represented by King, is surely gone, as shown by the fact it is still so exactly represented by King.

Don Henley had played beforehand. "We're going to do some ensemble singing," he announced. "Something you don't hear much these days. When people just seem to like... yelling." For a moment I thought he was going to tell the whole of Hyde Park to get off his lawn. Then he said he was digging out a rarely-played Eagles song, one that covered "the history of western civilisation in six minutes" and you knew it had to be 'The Last Resort', the darkest track from the very dark Hotel California album. It was, and it was quite something. That was written in 1976, and evidently it felt as if the culture to which he belonged was coming to an end. Yet a decade later it was coming to an end again, on 'The Boys Of Summer' with its, "Deadhead sticker on a Cadillac... 'Don't look back, you can never look back'". Predict the end for long enough and eventually you'll be right. Everything ends.

Everything ends, but art – we believe, we have to believe – continues. Which it does. But not always "our" art. "Our" music does not always renew itself. It too is mortal. The strange and novel will always arrive, but now it will arrive from somewhere else and we will connect to it differently. It may be that Carole King's own span has matched that of this kind of American pop; indeed, that she has outlived it. That's not a disaster. Such a span is just as natural in a cultural phenomenon as it is in a person. So we do look back, we forever look back, because that is where what we recognise, and what comforts us, is to be found – in the past. The present, so far as this music goes, is Carole King plugging the jukebox musical based on her work by welcoming its cast on to the stage. What was once all about invention and vision and pouring your life and heart into an unprecedented masterpiece is now all about leveraging accumulated familiarity. But the past, the past guided so thrillingly and movingly into the present, into tonight, is the superb show we've just seen, and a final, solo reprise of 'You've Got A Friend', which leaves us, firstly, in no doubt as to who King means by it and, secondly, in absolute bits.

Tapestry is, after all, a friend to every last person here. Which is why they're here. Everything ends. But not just yet, no, not quite just yet. One more moment of joy, at least – to brighten up even your darkest night.