Nearly 20 years have passed since two old Eton College chums had a long, tense telephone conversation about a plan one of them had concocted to have a man beaten up – unaware that someone was secretly recording them.

It has been known for years that the tape existed, and tantalising snippets have been leaked in the past, but now finally, a full transcript has come to light of that bizarre exchange between Boris Johnson and his friend Darius Guppy, who went to prison for masterminding a multimillion-pound fraud.

The Good Fairy must been present at Guppy's birth in 1964 to endow him with almost every quality a man could ask for, including wealth, good looks, ambition, intelligence and brilliant social connections. And the Bad Fairy must have been there too, to ruin the party by making him a psychopath.

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Guppy achieved notoriety in 1993 when he was jailed for an insurance fraud committed several years earlier, which came close to being a perfect crime. He and an associate paid someone to tie them up and fake a robbery in New York, so that he could claim £1.8m in insurance. It was his revenge on Lloyd's, the insurance firm which had ruined his father during a notorious financial scandal in the late 1980s.

After being released from prison he had a bloody confrontation with Earl Spencer, the brother of Princess Diana, who he believed had tried to seduce his wife while he was locked away. The allegation, which Earl Spencer vehemently denied, brought an end to the close friendship between the two old Etonians.

But it was three years before in 1990 that Guppy found infamy with Mr Johnson who was then the Brussels correspondent at The Daily Telegraph. At the time Guppy was a frightened man after a News of the World reporter, Stuart Collier, started inquiring into his background and he feared his dubious activities were about to be exposed.

Guppy wanted Mr Collier stopped, frightened and physically assaulted – and had lined up a mysterious south London figure to arrange it. However, one crucial part of the plan remained elusive – Collier's private phone number and address.

His attempts to persuade Mr Johnson – a fellow journalist – to help get it has never been released in full until now. It was recorded by Peter Risdon, a business associate of Guppy, who distrusted him so much he started secretly monitoring and recording his calls. The full transcript illustrates the Teflon quality of the London Mayor, who is able to emerge smiling from scandals that might have destroyed another politician's career, partly because it is difficult to know when to take him seriously.

The tape is also fascinating for what it says about Guppy, who has now vanished from the public eye. Of the many things written about him, few are as damning as the words he uses to describe himself. "Boris, can I tell you something," he is heard saying. "My honest opinion about myself is that I am a potential psychopath. The reason I am not a psychopath is because I have..."

"A mother?" Johnson is heard interjecting. "No, I have discipline over my feelings and it's as simple as that," he replied. "But I am telling you something, Boris, this guy has got my blood up all right, and there is nothing which I won't do to get my revenge. It's as simple as that."

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Guppy says he needs Mr Johnson to help trace Mr Collier's address because he has been unsuccessful in his attempts to do so and one of the London heavies who was to inflict the beating was becoming impatient. "I have just had a telephone call from this bloke, okay," he told Mr Johnson. "And I swear to you it is now getting to the stage where I am beginning to look stupid because I have been promising them for the past three weeks, and I cannot afford to look stupid."

Mr Johnson tried to reassure him: "These people are there to do your bidding. Just tell them it happens. You know – the trail is too warm, something like that."

Minutes later, Mr Johnson revealed that his anxiety that the man from the News of the World might find out that he was involved. "He is extremely dangerous, extremely dangerous," he is heard saying. "If you fuck up in any way, I mean frankly if he suspects that I am involved in this ... forget about me. Honestly, Darius, you have really got to think whether it's worth your while."

Mr Johnson then revealed that he had approached four people to try to get Mr Collier's details, only two of whom he could fully trust. "If it got widely known that he'd been beaten up, it would inevitably get back to the contact I've used," he said.

To reassure him, Guppy said: "Okay, right, may I just tell you what my plan is. My plan is this, that even once you give it to me I will leave it for one month before I do anything. It will happen in one or two months' time. All right?"

"You promise me that?" Mr Johnson is heard to reply.

Later in the conversation, Guppy repeated: "The deal is basically you furnish me the information, and I will put it on ice for one month." Mr Johnson then anxiously inquires: "How badly are you going to hurt this guy?"

Guppy answers: "Not badly at all."

The conversation goes on. Mr Johnson: "If this guy is seriously hurt, I am going to be fucking furious." Guppy: "I guarantee you he will not be seriously hurt."

Mr Johnson: "How badly hurt will he be?" Guppy: "He will not have a broken limb or a broken arm and he will not, er, he will not be put into intensive care or anything like that. He will probably get a couple of black eyes and a, and a cracked rib or something like that."

Mr Johnson: "A cracked rib."

Guppy: "Nothing which you didn't suffer in rugby okay but he will get scared and that is what I want him to do, I want him to get scared, I want him to have no idea who is behind it okay, and I want him to realise that he's fucked someone off and whoever he's fucked off is not the sort of person he wants to mess around with.

"Because I guarantee you Boris, I guarantee you these people are, you know, if someone hurts their boss or threatens their boss I promise you it's just total sort of, it's like they're like dogs, they are like Alsatians or rottweilers, they love their masters, they are affectionate towards them, they are evil bastards to everyone else."

Mr Johnson: "Yeah, yeah, good. Okay Darry now, yeah, I mean I but." Guppy: "You must have faith in me Boris."

After holding onto the tape for years, Mr Risdon was finally persuaded to release it to be broadcast on last night's Dispatches programme for Channel 4 – the same programme that ran a damaging investigation into Ken Livingstone's political associates. But he does not believe that the tape shows London's Mayor as having been involved in anything criminal. "My own feeling is that Johnson was just going along with Guppy, humouring him, and had no intention of helping."

But John Biggs, deputy leader of the Labour Group in the London Assembly, said: "This was not some youthful misdemeanour but a revealing insight into the moral code of the man who now leads our police. It appears that Boris was more worried about getting found out than the harm that would have been inflicted on one of his journalist colleagues."

After his release from open prison, Guppy emigrated to South Africa. An investigation by a Sunday newspaper two years ago found him living in a mansion with a swimming pool but with no bank account or visible means of support. He returned to London briefly last year for his mother's funeral but since then nothing more has been heard of the man who claimed that it was only self-control that saved him from being a psychopath. Dispatches spent months trying to track him down but with no success. For a man whose famous aquaintances have brought him infamy he seems to have decided an anonymous life is now for the best.

Darius and Boris: The conversation

Boris: How badly are you going to hurt this guy?

Darius: Not badly at all.

Boris: I really I want to know because ...

Darius: OK let me explain to you.

Boris: If this guy is seriously, I am going to be fucking furious.

Darius: I guarantee you he will not be seriously hurt.

Boris: How badly hurt will he be?

Darius: He will not have a broken limb or a broken arm and he will not, er, he will not be put into intensive care or anything like that. He will probably get a couple of black eyes and a, and a cracked rib or something like that.

Boris: A cracked rib.

Darius: Nothing which you didn't suffer in rugby OK but he will get scared and that is what I want him to do, I want him to get scared, I want him to have no idea who is behind it OK and I want him to realise that he's fucked someone off and whoever he's fucked off is not the sort of person he wants to mess around with. Because I guarantee you Boris I guarantee you these people are you know, if someone hurts their boss or threatens their boss I promise you its just total sort of, it's like they're like dogs, they are like Alsatians or rottweilers they love their masters, they are affectionate towards them they are evil bastards to everyone else.

Boris: Yeah. Yeah, good. Ok Darry now, yeah, I mean I but.

Darius: You must have faith in me Boris.