- Hank MarvinFormed / started: 28 October 1941Note: lead guitarist of The Shadows, songwriter
- Henry CluneyDecade started: 1950sGenres: rock music
- Henry McCulloughFormed / started: 21 July 1943Split up / ended: 14 June 2016
- Henry PriestmanBorn in: Kingston upon HullDecade started: 1970s
- Herbie FlowersFormed / started: 19 May 1938Split up / ended: 5 September 2024
- Hilton ValentineBorn in: North ShieldsDecade started: 1960s
- Hollywood BratsDecade started: 1970sGenres: glam punk
- Honest John PlainFormed / started: 12 April 1952Split up / ended: 13 June 2025
- Howard JonesFormed / started: 23 February 1955Note: English singer, songwriter
- Howard MossDecade started: 1990sGenres: rock music
- Hugh CornwellFormed / started: 28 August 1949Note: English rock musician
- Hugh HopperFormed / started: 29 April 1945Note: British bassist
- Humphrey LytteltonFormed / started: 23 May 1921Note: British jazz musician & broadcaster