The 73-year-old guitarist joined 60s group The Yardbirds as the 'Layla' hitmaker left in 1965, and has recalled Clapton inviting him to play at his concert in 1980, in his hometown of Guildford, where things first got tense between the pair.
On their first ''calamity'', Beck remembered: ''I remember he invited me to this gig [in 1980] in Guilford, near where he lives, and I thought, 'Why is he asking me?'
I thought to myself, 'Obviously you won't be playing, so go along and have a beer.'
''On the way there, he goes, 'Do you want to play 'Blackie'?' And I said, 'Uh, I don't know that song.'
He said, 'No, it's my guitar.'
I went, 'Oh, whoops.'
First calamity of the evening. So I said, 'I didn't bring a guitar, so I'll do that.'
''Then about a minute later, he turned around and stood at the car and goes, 'This is not gonna be one of these blowing-off things, is it?'
''I said, 'Listen, either I play or I don't.' And there was that, what's the word, uncomfortable rivalry about it.''
The 'Hi Ho Silver Lining' hitmaker says that their fierce competition went to new heights when Clapton heard that Beck was involved in Stevie Wonder's hit song 'Superstition' in 1972, something he claims he learnt from the 73-year-old rocker's ex-wife, Pattie Boyd.
He said: ''I found out later from Pattie, his wife, that there definitely was [rivalry] - especially with the Stevie Wonder stuff. He was not too amused about me doing something successful with Stevie. I think that maybe got under his skin a bit.''
Their rivalry soon waned out, and Beck admits he was ''overwhelmed'' that Clapton spoke kindly of him for the new documentary about his life, 'Still on the Run: The Jeff Beck Story', which also features commentary from Led Zeppelin's Jimmy Page and Gun N' Roses' Slash.
He told Rolling Stone magazine: ''I must admit there was a tear [laughs] especially with Eric. I never expected him to bother to be in it. I studied his face over and over, just to make sure there wasn't something else going on [laughs]. But no, it was just overwhelming.''