Thousands are expected to demonstrate against Bush, who will stay at Queen Elizabeth's London residence, Buckingham Palace, visit Blair's northern English constituency and talk with relatives of British soldiers killed in Iraq.
"I can understand people not liking war, if that's what they are there to protest," Bush told the British news agency the Press Association and the Daily Telegraph and Financial Times newspapers in an interview published on Friday.
"I fully understand not everybody is going to agree with the decisions I've made."
Blair's public ratings have plunged over war in Iraq, which most Britons opposed. Mounting guerrilla resistance seven months after the fall of President Saddam Hussein has raised fears of more British casualties beyond the 20 already killed in combat.
Bush said he would take the opportunity to explain his Iraq policy, which he said aimed to keep America secure and create around the world "free societies ... which do not breed terror".
A poll of British voters this week showed 60% disapproved of Bush's handling of Iraq, while only 40% thought Blair's close ties with Bush were good for Britain.
Still shoulder to shoulder
Bush went out of his way to compliment his closest international ally and denied he slavishly followed Washington.
"I have never heard him complain about the polls or wring his hands. The relationship is a very good relationship because I admire him and I admire somebody who stands tough," he said.
Bush said both he and Blair thought the Iraqi people were "plenty capable of running their own country", a signal perhaps that a faster handover of power is under active consideration.
UK government insiders have speculated that Bush will reward Blair for his staunch support since the September 11 attacks.
Thousands plan to demonstrate against Bush's invasion of Iraq
One possibility would be an announcement on British soil that the United States will lift tariffs protecting its steel industry which this week were declared illegal.
"I am listening, looking and we will decide at an appropriate time," Bush said.
The president said he would meet the families of some UK soldiers who lost their lives in Iraq and deliver two messages.
"One, the prayers of the American people and prayers of the president are with them as they suffer," he said.
"Secondly, I will tell them that their loved ones did not die in vain. The actions we have taken will make the world more secure and the world more peaceful in the long run."
Handover in Iraq
On Thursday, Condoleezza Rice, Bush's national security adviser, confirmed that the president, after two days of talks with US Iraq administrator Paul Bremer, was now considering ways to hand Iraq over to the Iraqis before a formal constitution is written.
While Rice said it remained essential for Iraq to have a permanent constitution and elections for a permanent government, "What is also as important is that we find ways to accelerate the transfer of authority to the Iraqi people. They are clamouring for it. They are, we believe, ready for it. And they have very strong ideas about how that might be done."
Bush told reporters in the Oval Office he wanted the effort to "encourage the Iraqis to assume more responsibility."
An early hand over of power was previously rejected by the United States in favour of having the US-established Iraqi Governing Council write a constitution, then hold elections before power would be transferred.