As early as mid-2002, then-British defence minister Geoff Hoon told a key government meeting that US forces had begun "spikes of activity" to put pressure on the regime, the Sunday Times said.
The newspaper printed minutes from a gathering of Prime Minister Tony Blair and his war cabinet in July 2002 on the build-up to a possible conflict.
According to the minutes, Blair was told that in Washington, war was even then seen as "inevitable" and that "the intelligence and facts were being fixed around the policy".
Blair was the United States's staunchest ally in the later invasion of Iraq, launched in March 2003.
The Sunday Times newspaper said that separate information obtained by the Liberal Democrats, a British opposition party which opposed the Iraq war, showed that British and US planes dropped twice as many bombs on Iraq in the second half of 2002 as they did during the whole of 2001.
The minutes of the 2002 meeting also show British ministers' efforts to justify full-scale military action.
"It seemed clear that (US President George W.) Bush had made up his mind to take military action, even if the timing was not yet decided," they said.
"But the case was thin. Saddam was not threatening his neighbours, and his WMD (weapon of mass destruction) capability was less than that of Libya, North Korea or Iran.
"We should work up a plan for an ultimatum to Saddam to allow back in the UN weapons inspectors. This would also help with the legal justification for the use of force."