Before emigrating from England to the USA to play with Miles Davis on his seminal and quite controversial
Bitches Brew era "jazz" releases John also gave lessons to a young guitar student named Jimmy Page and played in a jazz combo with Jack Bruce on upright bass before Jack switched to playing electric. That was before any bands named Cream or Led Zeppelin existed.
That would be the Graham Bond Quartet in 1963 IIRC. Bond, originally an alto sax player, left Alexis Korner's Blues Incorporated* to form his own band, taking Korner's rhythm section (Bruce and Ginger Baker, who had replaced Charlie Watts) with him. McLaughlin rounded up the combo until Baker had him fired for being, in Ginger's words, "a whiner and a miserable moaner"... John was replaced by the late, great Dick Heckstall-Smith on tenor and soprano, while Bond switched to organ (he was a pioneer of the Hammond in Britain, and influenced all the prominent players in the scene: Brian Auger, Jon Lord, Georgie Fame, Alan Price, you name it - McLaughlin also had stints with Fame and Auger). The band's name accordingly changed to 'The Graham Bond ORGANisation'. The line-up lasted until Baker convinced Bond to also fire Jack because his style was, wait for it, "too busy", and carry on without a bass player. For the next few gigs Bruce kept coming to play and get paid, until Baker pointed a knife to his belly and said "If you show up one more time, this goes in you".
(Of course, he had to relent one year later when Clapton accepted to form a band with him on condition that he convinced Jack to be on board - Eric had played with Bruce when the latter replaced John McVie for a while in John Mayall's Bluesbreakers.)
Other Bond alumni include two incredible drummers, Jon Hiseman who went on to form Colosseum with Heckstall-Smith and John 'Pugwash' Weathers, later of Gentle Giant. Graham also played in some of Bruce and Baker's post-Cream projects. McLaughlin too raised some money for his trip to America to take part in the
In a Silent Way sessions by recording about half of the tracks in Bruce's free jazz album
Things We Like (again with Heckstall-Smith and Hiseman, and Jack on the upright - it was his first solo album but was released after
Songs for a Tailor). They later reconnected when Bruce was asked to join Tony Williams's Lifetime.
I could go on for days with this stuff. The friends-and-family tree of John Mayall collaborators is often deservedly brought up in rock histories, while that other veritable Who's Who of British jazz and pop heroes that is the list of Alexis Korner associates is much less so (I'd flat out call him nearly as essential to the development of British pop as the Beatles were). Colosseum's connections are also sizable.