Woolf Phillips[1] was the bandleader and MC at the London Palladium during the Golden Age of Variety and arranged and conducted for Judy Garland, the Marx Brothers, Frank Sinatra, Nat King Cole, Duke Ellington, Benny Goodman, Danny Kaye and Dean Martin, among others, while Sid Phillips wrote for the Bert Ambrose Orchestra, played in Louis Armstrong's British All Stars, and led Britain's best known Dixieland Band.

[2] While enrolled at the University of Sussex he was involved in session work and gigs with Peter Green, members of Fleetwood Mac, Kevin Ayers, and John Martyn.

[3] He also played saxophone with such artists as Jimi Hendrix, Bob Marley, Eric Clapton, Phil Collins, Little Richard, and Van Morrison for whom he functioned as arranger and musical director as well as reed player.

Among his hit records have been Aled Jones' Walking in the Air (which he also produced); Alison Moyet's That Old Devil Called Love, Simple Minds Street Fighting Years, Rod Stewart's Downtown Train, George Michael's Kissing a Fool, Prefab Sprout's Hey Manhattan, Tina Turner and Barry White's Wildest Dream, Diana Ross' Christmas Album, Björk's It's Oh So Quiet, Goldie's Saturnz Return.

He was musical director for the All-Star Band assembled for the 1981 Amnesty International benefit show The Secret Policeman's Other Ball – an ensemble that included Sting, Eric Clapton, Jeff Beck, Phil Collins, Bob Geldof, Donovan and Midge Ure.

In the jazz world he has performed with Chet Baker, Plas Johnson, Ernie Watts, Red Holloway, Conte Candoli, Slim Gaillard, Barbara Morrison, Herb Geller, Wild Bill Davison, Bud Freeman, Les McCann, Percy Heath and many others.

Personnel includes Wayne Bergeron, Andy Martin, Pete Christlieb, Grant Geissman, Gary Foster, Warren Luening, Peter Erskine, Alex Acuna, and Tom Ranier.

Altman is a frequent guest conductor for the Royal Philharmonic Orchestra, and served on the board of ASMAC (the American Society of Music Arrangers and Composers), and as a member of the governing Council of the British Academy of Film and Television Arts (BAFTA).

He was also co-founder – and co-host for seven years – of the "10 Room" Monday night jam session in London which won Club Night of the Year awards – and featured guests such as:Pharrell Williams Lionel Richie, Macy Gray, Will Smith, Black Eyed Peas, Alicia Keys, Najee, Wyclef Jean, Shaquille O'Neal, the Roots, The Neptunes, Mario, Roy Ayers, Omar, Chaka Khan, Chris Tucker and the Backstreet Boys, as well as helping to launch the careers of John Legend, Katie Melua, Gabriella Cilmi, and Amy Winehouse, who was a regular 10 Room habitué and performer.

His association with Monty Python had started when he appeared on the album Matching Tie and Handkerchief, and continued when he arranged the music for the Rutles television special All You Need Is Cash created by Eric Idle and Neil Innes.

Thus far his guests have included Sanjeev Bhaskar, Michael Palin, and Goldie with Rob Brydon, Jim Carter, Imelda Staunton, Lenny Henry, Adrian Dunbar, and Bradley Walsh kicking off 2019's guest list.In 2023 he arranged all (and composed some of)the period music for the movie Shoshana directed by Michael Winterbottom Altman is the most prolific writer of music for commercials, having scored more than 4,000 TV advertisements.

He is also a prolific composer of library music, with his work being featured worldwide in movies and on television, in productions such as Peaky Blinders,America in Colour and Dancing With The Stars.