Final answer:
The British Prime Minister who worked closely with President Bush during the War on Terror was Tony Blair. They collaborated during the Afghanistan and Iraq invasions.
Step-by-step explanation:
The British Prime Minister who allied himself with President George W. Bush during the War on Terror was Tony Blair. After the tragic events of September 11, 2001, President Bush initiated a global campaign against terrorism, demanding that countries turn over terrorists or face the consequences.
The United Kingdom, under Prime Minister Tony Blair's leadership, was a staunch ally of the United States in this effort, particularly during the invasions of Afghanistan in 2001 and Iraq in 2003.