In New York, you can eat sushi in a basement café opposite Patti Smith, or have a door held open for you by Colin Farrell. In London, however, spotting a celebrity ranks up there with seeing someone, as I did a few weeks ago, strolling nonchalantly down the street with their breasts on show. That is, amazing when it happens but not an everyday occurrence.

We're used to a bit of distance between ourselves and celebrities. The Greeks had oracles to intercede for them; we have journalists: there's a whole rung of middle-men, messengers, mouthpieces and mongers to put a slant on the musings of the pedigree pensées of those Olympians, the rich and the famous.

I'm as much of a sucker as anyone for celebrity gossip – although I try to limit myself to the Not Tacky Kind. So you'll have to take any questions about Kerry Katona elsewhere, thank you very much. But I do like to know about their haircuts, their relationships, their houses and, sometimes, their children. Imagine my paroxysms and self-hugging, then, when I ended up in a whole convoy of the creatures at a festival last week.

The celebrity in the wild is a guarded and defensive animal, delicately and deliberately placing one foot in front of the other in case the paparazzi come streaming over the plains. To see them in a more domestic setting – that is, among their own – is quite a different matter.

What's strange about celebrities is that they all get on with each other, regardless of creed, colour, taste or international popularity. We learnt that from Celebrity Big Brother: they're comrades in a club that is tired by the attentions of the hoi polloi. Watching them together is like going to the zoo and seeing all the animals that aren't lions or tigers braiding each other's fur, simply because they're in this together. And when the lions – that is, the press or Joe Public – approach, they huddle closely for security, a rich mix of incongruous feathers, beaks and flippers.

But another facet of fame – and this is why they all get divorced, I think, those Hollywood stars – is that celebrities lose all sense of self-awareness and turn into Nero, determined to make their horse a senator, to Hell with anyone who points out it's got four legs and whinnies.

I found this out while chatting to a Rock Music Legend during my trip. A gaggle of Normals were sitting around a table and it was sheer coincidence that I ended up next to him. But we talked for a while about concepts from synaesthesia to safety coffins. You have to talk about abstruse and rarefied things like this when you're a celebrity, you see, because you don't want to alienate your lowly audience. They spent their Sunday watching Come Dine with Me, while you spent yours on a private jet and serenading thousands in a stadium.

Every time our chat even hovered near the boundaries of this man's fame, he demurred and flapped his hands to indicate he didn't want to talk on those terms. But just as I was about to make my most interesting point about safety coffins (that some of them come with an emergency flare, but what use is that when you're buried alive, I ask you?), we were rudely interrupted. Another celebrity had arrived, a Famous Young Actress, and she stepped straight into the conversation. Would it be the nirvana of fame, two über-celebs talking to each other like an average civilian?

"Oh!" she declared to the Rock God Legend, in the stilted sententiae of the chorus in a Greek tragedy. "I wanted to tell you that I was thinking that I might maybe buy your new album. I like the sound of it from what I've heard, and I am a person who likes music."

"Why, thank you Famous Young Actress," returned the Rock Music Legend. "That means so much to me. For I know that you are indeed a person who likes music."

Us plebs didn't know where to look. "Why don't they just talk like ordinary people?" we all wondered, at first. Then: "How on Earth did she see fit to interrupt three separate conversations to say that?"

It's odd, tweaking the skirts of celebrity and seeing their feet of clay. They're just banal and slightly awkward people, relating to each on the only terms they know: either obseqiousness or indifference. Because that's what we treat them with, and that's all they know. I was happy when the Rock Music Legend returned to our conversation about coffins. "When I die," he said, "I want to be scattered across three continents."

Which was arguably the most glamorous thing he said throughout the festival, but also the most genuine.