We were eating in a restaurant in New York City. Yoko was with us, so this was after their big break-up and reconciliation. Yoko was expecting their child, Sean, and John was excited — he was going to love this baby day and night: feed him, change him, teach him to talk, teach him to love music.

He did all of that. And he was going to watch him grow into adolescence, through the tumbles from bicycles and terrors of schooldays, from reading to dating to college. He never got to do that. John started talking about UFOs.

He said he believed life existed on other planets, that it had visited us, that maybe it was observing us right now. He took me to a quieter, darker table, lit a cigarette and pointed its glowing tip at my face.

“You believe in this stuff, right?” he asked me. “Well, you ain’t f—in’ gonna believe this.

“About six months ago, I was asleep in my bed, with Yoko, at home, in the Dakota Building. And suddenly, I wasn’t asleep. Because there was this blazing light round the door. It was shining through the cracks and the keyhole, like someone was out there with searchlights, or the apartment was on fire.

“That was what I thought — intruders, or fire. I leapt out of bed, and Yoko wasn’t awake at all, she was lying there like a stone, and I pulled open the door. There were these four people out there.”

“Fans?” I asked him.

“Well they didn’t want my f—in’ autograph. They were, like, little. Bug-like. Big bug eyes and little bug mouths and they were scuttling at me like roaches.”

He broke off and stared at me.

“I’ve told this to two other people, right? One was Yoko, and she believes me. She says she doesn’t understand it, but she knows I wouldn’t lie to her. I told one other person, and she didn’t believe me.

“She laughed it off, and then she said I must have been high. Well, I’ve been high, I mean right out of it, a lot of times, and I never saw anything on acid that was as weird as those f—in’ bugs, man.

Friends: Lennon and Geller in conversation

I was straight that night. I wasn’t dreaming and I wasn’t tripping. There were these creatures, like people but not like people, in my apartment.”

“What did they do to you?” Lennon swore again. “How do you know they did anything to me, man?” “Because they must have come for a reason.”

“You’re right. They did something. But I don’t know what it was. I tried to throw them out, but, when I took a step towards them, they kind of pushed me back. I mean, they didn’t touch me. It was like they just willed me. Pushed me with willpower and telepathy.”

“And then what?”

“I don’t know. Something happened. Don’t ask me what. Either I’ve forgotten, blocked it out, or they won’t let me remember. But after a while they weren’t there and I was just lying on the bed, next to Yoko, only I was on the covers.

“And she woke up and looked at me and asked what was wrong. I couldn’t tell her at first. But I had this thing in my hands. They gave it to me.”

“What was it?” Lennon dug into his jeans pocket. “I’ve been carrying it round ever since, wanting to ask somebody the same question. You have it. Maybe you’ll know.”

I took the metal, egg-like object and turned it over in the dim light. It seemed solid and smooth, and I could make out no markings. “I’ve never seen anything like it.”

“Keep it.” John told me. “It’s too weird for me. If it’s my ticket to another planet, I don’t want to go there.”

When we first met on November 28, 1974, almost exactly 30 years ago, he was suffering terribly from his separation from Yoko. His drug abuse and drinking, linked to the sorrow of Yoko’s recent miscarriage, had driven them apart, and John desperately wanted to mend the relationship.

He just didn’t know how to make the first move. The night Lennon and I were introduced, Elton John was playing at Madison Square Gardens. Elton was trying to persuade the ex-Beatle to get up on stage with him, and John was torn — he wanted to perform but he was scared.

Finally, he turned to me and offered a deal, as though I were a negotiator sent by God: “I’ll sing,” he said, “but you have to make Yoko call me.”

Like all of John’s jokes, this one was a plea from the heart, wrapped in a sardonic quip. Yoko phoned John out of the blue, 36 hours later. I think John always believed I had beamed a mind-control ray at her. For my part, I think that of all the synchronicities that have shaped my life, that was one of the strangest.

John Lennon was a compulsive doodler. The last autograph he ever signed, 15 minutes before Mark Chapman gunned him down outside his home at the Dakota Building, on December 9, 1980, features a double portrait of himself and his wife, Yoko Ono. The drawings are done in a couple of lines — the style is unmistakable and so are the faces.

I always marvelled at John’s skill as an artist. There is no doubt that, if he’d been tone deaf and tuneless, the boy who created The Beatles could have become a successful painter or illustrator. During the last year of his life, we met most weeks to chat over a coffee in one of the hotels near our New York homes.

Sometimes John would bring Sean, who was about four years old then. The rocker had put his music career on hold while the child was small. John once told me how bitterly he regretted that while his first son, Julian, was a toddler, he himself was devoting his energies to the stage or the studio, or would be out partying with friends.

“You don’t get those years back,” he said. “I’m not going to miss a minute while Sean is growing up.”

That is the greatest tragedy of my friend’s death. He had finally learned what made him happy, and then he was robbed of it. What really interested me about John was not his incredible life, his fame or his talent, but his deep spirituality.

I too was working out what made me happy — I’d realised at last that buying watches and eating six helpings of dessert before making myself throw up was not the path to nirvana.

The shock of Lennon’s murder was one of the powerful forces that drove me to quit New York and spend a year in Japan, undergoing a spiritual detox. John spoke with passion about Japanese views of life, and I am certain that Yoko’s philosophies were at the core of his last years.

I was woken on the day John was shot by a call from a friend, Roland, a publisher who lived opposite the Dakota.

“He’s dead,” Roland sobbed. “They killed John.” I dressed in a few seconds and ran across town: somehow I had to see the house to believe the news. The radio reports weren’t enough.

If John really were dead, if this wasn’t some sick media hoax, then there would be people outside his home with candles and prayer bells. They were there, in their hundreds already.

I didn’t have to push my way through the crowd; I simply stood and stared across the road, and then walked away through Central Park with the tears running down my face.

Now, 24 years on, when I hold the cold, metal egg in my fist, I have a strong sensation that John knew more about this object than he told me. Maybe it didn’t come with an instruction manual, but I think John knew what it was for.

And whatever that purpose was – communication? healing? a first-class intergalactic ticket? – it scared him. I wish I could have warned him . . . that however scary aliens seem, it’s the humans you have to fear.

· ‘Uri’s Haunted Cities: Venice’, Sky 1, January 9, 9pm