To answer the original question,
At the end of WWII, War crimes were divided into three broad categories.
a) Crimes against Peace. Initiation of invasions of other countries and wars of aggression in violation of international laws and treaties.
b) War Crimes. Atrocities or offences against persons or property including, but not limited to, murder or ill treatment of prisoners of war or persons on the seas, the killing of hostages, plunder of public or private property, wanton destruction of cities, towns or villages, or devastation not justified by military necessity.
c) Crimes against Humanity. Atrocities and offences, including but not limited to murder, extermination, enslavement, deportation, imprisonment, torture, rape, or other inhumane acts committed against any civilian population.
Your question concerns the first category. Those liable for indictment under the first category are the heads of state and their cabinets, ministers of the armed forces and the senior military leadership of the offending nation.
In this case, however, the U.N. sanctioned war against Iraq prior to Desert Storm. Fighting ceased under the terms of a U.N. ceasefire resolution passed under Chapter VII of the UN Charter, allowing the use of force. Since Iraq has never complied with the ceasefire provisions, the war has not ended and the outside world is still entitled to resort to military force.
The only question remaining is, has Iraq ever been declared in violation of this and subsequent resolutions? And the answer is yes, several times. e.g.
Resolution 707 - Aug 15, 1991
The Security Council issued a strong denunciation of Iraq's "serious violation" of its promise to co-operate fully with Unscom and told Baghdad it was "in material breach" of Resolution 687.
June 1996.
In a Security Council Presidential Statement, the U.N. the condemned Iraq for clear and flagrant violations of resolutions 697 (1991), 707 (1991) and 719 (1991)...........
Iraq Index
So, legally, Bush and Blair seem to have a sufficient case to proceed and to justify it in court. The same case was used as the basis for the establishment of the No-Fly Zones and the subsequent air attacks which have been conducted ever since, the validity of which has been accepted by the international community.