The same source.
'But then I noticed his hands were shaking as if he had Saturday night palsy. He had the worst hangover I'd ever seen. And he was obviously terrified of me. I just took pity on him. I realised he really was human. That was the beginning of our affair.'
From their first screen embrace, it was plain that she and Burton were more than just good friends. The director Joseph Mankiewicz, aware of the potential for scandal and trouble, cabled the studio: 'I want to give you some facts you ought to know. Liz and Richard are not just playing lovers - they are lovers.'
Many predicted that their shenanigans during the making of the epic - they almost bankrupted 20th Century Fox - had alienated the public, and their careers were finished. Instead, they became the hottest couple in Hollywood.
According to Eddie Fisher, Burton told him: 'You're a star already. I'm not. Elizabeth is going to make me a star.' I don't know whether Burton was that calculating - but if he said it, he spoke only the truth.
Their next film, The VIPs, in which they played a husband and wife, was a huge box-office hit.
It proved, he said, his theory that 'if you are going to make rubbish, be the best rubbish in it. You've got to swank in Hollywood.
'Now when I go there I demand two Cadillacs - one for my family - and the biggest dressing-room in the studio. Of course, I'm not worth it, but it impressed them.'
Not everyone approved of Burton's success. Larry Olivier warned him: 'Make up your mind. Do you wish to be a household word or a great actor?' His agent was appalled, accusing him of selling out and trying to 'get recognition on a trick'.
Burton didn't give a damn. He was collecting $500,000 a movie - he got $150,000 to play Marc Antony and make love to Elizabeth Taylor in Cleopatra.
'Not bad for a spoiled genius from the Welsh gutter, a drunk and a womaniser,' he told me with satisfaction, as he sipped 'an unwinding jar of nectar' after a day spent filming Becket on a bitterly cold beach in Northumberland.
It was a long way from the mining village of Pontrhydyfen, South Wales, where he was born Richard Jenkins in 1925, the 12th of 13 children of a hard-drinking coalminer whose chief possession was a gift for words.
Two of Burton's sisters died before he was born. His younger brother was five days old when their mother died. Burton was two.
'The whole family was an immense kinship, but as far as we ever admitted our affection for each other was to say: "Well, blood is thicker than water."
'We were a funny lot. I didn't speak English until I was ten, when Philip Burton, the schoolmaster who became my guardian, took me under his wing. I took his name when I became an actor.
'Now here I am working with Peter O'Toole and the great Sir John Gielgud, two of the finest actors in the land.
'I'm sleeping with Elizabeth Taylor, the most famous and beautiful movie star in the world. I've not got a lot to beef about.'
There was already talk that the three actors - Burton, O'Toole and Sir John Gielgud - were giving the best performances of their careers in Becket. (They each received an Oscar nomination; Burton received seven in his career, but did not win the award once.) But what pleased him most was that Gielgud had called him 'Dick' that morning.
'The old bugger has never called me Dick before. Isn't that strange? I've known him forever. "The two finest Hamlets of our generations," they say. But he has always called me Richard. Often simply Mr Burton.
'He is very formal, very Victorian. He doesn't entirely approve of me. He thinks I'm too wild and have scandal around me all the time. But now suddenly I'm Dick. I feel I've finally made it.'
At dinner the following evening, Burton and O'Toole (who was playing Henry II), got into a tipsy argument about fame - they were very competitive - when Sir John had mischievously asked which of them was the most famous. It was the kind of argument that Burton relished, and which challenged O'Toole's Irish wit.
Burton said that he was the most famous - Time magazine had called him 'the demi-Atlas of this earth' - and he probably was.
O'Toole countered that Burton was only half-famous - Elizabeth was the other half.
They continued to attempt to top each other until the early hours, telling increasingly wild stories about their triumphs - as actors and lovers - and the poverty from which they came.
At 4am, I was woken by a ringing phone. 'I may be only half-famous, but I've got the other half snoring very contentedly in bed next to me. O'Toole can't top that,' Burton chortled happily, and rang off.
He finally married Taylor in 1964. But it was always a tempestuous relationship.
'Our love is so furious that we burn each other out,' he said. In 1974, they divorced. In 1975, they married again.
But in and out of love, they lived extravagantly. They bought a yacht, the Kalizma, for $500,000, an immense sum in the Sixties. He bought her a 33-carat Krupp diamond for $305,000; a $1million, 69-carat Cartier diamond; and the La Peregrina Pearl that Philip of Spain had given Henry VIII's daughter, Mary Tudor, in 1554.
'It's only money, luv,' he told me. But the writing was on the wall, and it no longer said 'Dick loves Liz'. Once, he dropped by my house for a drink. He had quarrelled with Taylor because they could not decide which restaurant to go to for dinner, and he had stormed out of their suite at the Dorchester.
Although I knew the marriage was rocky, I was still surprised when he offered to buy my house - for a love nest. Later, when he came to dinner with Taylor, she told him: 'This place is too big for a love nest. It'd make a fine harem, though - but you're not up to that any more, Buster.'
I was astonished. Why had he told her about the love nest? 'It keeps her on her toes, luv,' he said.
But in 1976, the days of wine, roses and million-dollar trinkets were over between them for the final time. Insisting that he was lost without a woman in his life, he promptly married the model Suzy Hunt. It ended in 1982, after six years.
'She was a nice girl, but she cost me a million dollars and my second house in Puerto Vallarta when we parted. Elizabeth got the first one in our first divorce,' he said.
'Expensive business, divorce. But God put me on this earth to raise sheer hell. And I guess women are part of it.
'I only drink when I'm working,' he had always insisted, and he was now working harder than ever, for less and less money. It showed.
'He is no longer in charge of his face,' complained one critic, appalled at his dissipation, and noting the way his 'little piggy eyes glisten and swivel' in his seamed and immobile face.
I continued to meet him around the world: New York, Paris, Mexico and aboard the Queen Elizabeth.
In Hollywood, after a few drinks too many at the Sportsmen's Lodge - he was making Exorcist II: The Heretic, a dreadful film, at Warner Brothers - the manager refused to give him the keys to his car. While I was calling for a taxi, he accepted a lift from a couple of besotted fans who, halfway across Coldwater Canyon, became apprehensive about their passenger, who was entertaining them with songs from Camelot.
'Something about insurance, luv. I made them nervous. They insisted I get out and walk,' he told me the next day.
He tried thumbing a lift back to Beverly Hills, but nobody would stop for him. He was forced to walk all the way home.
It was the moment that he felt his fame was over. In fact, his fame never ended, though his career dwindled in a series of increasingly poor films and drunken episodes, long before his death from a cerebral haemorrhage. He was 58.
Not long before he died, we talked on the phone. Married for the fifth time, to Sally Hay, a make-up artist, he was on the wagon again and was talking optimistically about the future.
'I've got a touch of cirrhosis of the liver, but that's to be expected. It'll be a little longer before they write my epitaph,' he said.
I asked him what it would be. He laughed, and quoted Keats: 'Here lies one whose name was writ in water.' .
Nevertheless, for his performances in The Spy Who Came In From The Cold, with Taylor in Who's Afraid Of Virginia Woolf, his role as an unfrocked priest in The Night Of The Iguana, Becket and The Taming Of The Shrew, again with Taylor - and never having won an Academy Award, despite those seven nominations - he will always be remembered as the fine actor he once was.
And I will always remember him as a friend. A rollicking, fascinating, roguish and talented friend who drank too much and died too soon.