They headed first to Washington DC, dropping in on gospel choirs and meeting the singer Joe Williams backstage at the Paramount Theatre in Philadelphia. Next they covered the eastern seaboard, jazz's early homes of New Orleans and Chicago, the "territory band" states of the Carolinas, on to Memphis and St Louis, and then Kansas City, where they found Charlie Parker's mother still too overcome by her son's death five years earlier to talk to them.
The journey was as much about the life around jazz, so Claxton was keen to cover the street scenes during New Orleans's renowned funeral parades. "I'd have two cameras around my neck, one colour, one black and white," he says. "After the funeral they'd come out of the graveyard playing jazz, and everyone would share in it." He captured the "secondliners" - "street toughs who can't play instruments but dance with parasols" - by running ahead, stopping to compose his shot, and then jogging in front again. "I think I lost four or five pounds in two days through perspiration," he recalls.
In Chicago, Claxton enjoyed a plate of chilli made by the trombonist Jack Teagarden at 5am; when the house was raided by the police, they joined in the "breakfast" too. But late hours was something Claxton got used to, which made an afternoon pool party on the West Coast wing of their trip something of a novelty.
The vibraphonist Terry Gibbs agreed to host the gathering at his North Hollywood home, and a group including the pianists Wynton Kelly and Horace Silver and the bassist Paul Chambers turned up. "Many of them said they'd never seen a swimming pool in the sunlight before," says Claxton. The white guests, he remembers, showed up very pale indeed in their swimwear. "Even in California, where everyone ate health food, the musicians were nocturnal."
Photographing Thelonious Monk in San Francisco for an album cover, Claxton had to rouse the pianist from his bed - at three in the afternoon. "The producer wanted a picture of Thelonious on one of the cable-cars," says Claxton. Monk groaned when he heard the idea, so the photographer suggested they go for a drink. "I saw a sign saying 'champagne cocktails', and asked if he'd had one. 'What's a champagne cocktail?' he replied. But after a couple of those we had a great rapport. That's why he's smiling."
Although he shared their hours, Claxton did not join the musicians in all of their habits. "I'd be taking photographs," he says, "and people right next to you would be shooting up heroin or speedballs. They knew I was one of the hip people; I wasn't the 'fuzz', or the 'heat'. But if the needle was passed to me I'd just say no."
Not that Claxton was averse to other substances. "I loved pot, and it helped that I met Aldous Huxley around that time. He'd invite some friends over, we'd try a little mescaline, a little marijuana, a doctor would take our blood pressure, and then we'd go out into the garden and get hung up over flowers."
It was a time of experimentation, when the new sound of hard bop was evolving from the bebop revolution of Charlie Parker and Dizzy Gillespie. But the older styles thrived around New Orleans, and the big bands, although past their heyday, still toured. The day when pop music brought success to small bands such as the Ramsey Lewis Trio, through covers of chart hits, but dealt a terminal blow to large ensembles, had not yet arrived.
Claxton could photograph Bill Evans in a Hollywood club, locked in concentration at the piano, his head barely above the keyboard. Or he could record the massed horns of Duke Ellington's orchestra at the Monterey Jazz Festival. The longstanding stars were still with the Duke - Paul Gonsalves on tenor, Johnny "Rabbit" Hodges on alto, and at the end you can almost hear Ellington introduce the section's anchor in his customary fashion: "all-American No 1 baritone saxophonist, Harry Carney".
"Whenever I met musicians that I didn't know," says Claxton, "I'd spend time watching their body language, how they held their instruments, how the light hit their faces. I'd try to make myself as unnoticeable as possible."
Claxton is 78 now, and many of the friendships he formed have been sundered by death; that with Ellington, for instance, or with Miles Davis, whom he managed to photograph in a pose rare for the trumpeter - smiling. "I had the good fortune to meet him when I was quite young, and so was he, in 1950," says Claxton. "We were introduced on the street by a musician named Alan Eager. He said, 'This is my friend Clax,' because that's what he called me. Miles said, 'Clax? Sounds like a household cleaner.' So we had a laugh right away."
A new book, from which these images are taken, provides a beautiful record of that time, and of the different sources of what Claxton calls that "one great American music". "To me, so much of jazz sprung from soul, blues, church music and folk," he says. So Will Shade in Memphis, with his "tub bass" made from an oil drum, a rope and a broomstick, was as much a part of the journey as trumpeter Clark Terry, relaxing at the NBC studios, or "Wolfman", the blues singer, in a Southern prison.
"You've got to remind people that this was another era," recalls Claxton. "But they were wonderful sounds."
All pictures from 'Jazz Life' by William Claxton, published by Taschen at £100. To order a copy at the special price of £90 (including delivery), call Independent Books Direct on 08700 798 897Reuse content