Direct proof of use
Royal Air Force squadron history records 617 Squadron contributing to the Tornado GR4 force deployed for Operation TELIC, flying missions against Iraqi targets from Kuwait and conducting the first operational Storm Shadow mission on 21 March 2003.
A Royal Air Force Air Power Review account of Operation TELIC describes the GR4 force mounting the first Storm Shadow missile attacks during the short opening phase of pre-planned missions, with the missiles chiefly aimed at key nodes in Iraq's integrated air-defence system.
Sources: 617 Squadron, The RAF in Operation TELIC, Air Aspects of Operation Iraqi Freedom
Timeline
The first documented milestone is the 21 March 2003 mission recorded by 617 Squadron. Air Power Review places the first operational use on the night of 21-22 March and identifies the launch aircraft as the Tornado GR4.
By 23 March, RAF GR4 and GR7 aircraft were being shifted largely toward kill-box interdiction and close-air-support tasking, while Storm Shadow remained one of the documented fixed-target and interdiction capabilities used by the Combat Air Wing.
Sources: 617 Squadron, Air Aspects of Operation Iraqi Freedom, The RAF in Operation TELIC
Narrative
Storm Shadow entered combat service with the United Kingdom during the 2003 Iraq War as an air-launched standoff weapon carried by RAF Tornado GR4 aircraft. Its documented operator in the conflict was the Royal Air Force, which flew the missions as part of United States and coalition forces.
The weapon's supported role was opening-phase long-range strike and interdiction. RAF analysis says the GR4s used Storm Shadow alongside more conventional Paveway laser-guided bombs during the first pre-planned missions, and that the missile attacks chiefly targeted Iraqi integrated-air-defence-system nodes.
Imperial War Museums metadata for RAF Mobile News Team footage from Ali Al Salem Air Base records Storm Shadow missiles being fitted to a 617 Squadron Tornado GR4 in 2003, matching the Kuwait-based operating context in RAF squadron history. Later RAF analysis described the operation as a valuable live operational test for Storm Shadow, while noting that many deployed missiles were development examples rather than the finished article.
Sources: 617 Squadron, The RAF in Operation TELIC, Operation TELIC 1 RAF Mobile News Team Tape 57