LONDON — Heading into two days of talks, President Bush and British Prime Minister Gordon Brown plan to discuss what progress is needed in Iraq before more U.S. and British forces can return home.

Their meetings amount to another get-to-know-you session between two leaders confronting their own woes at home.

Bush, who remains widely unpopular in Britain as he is in the United States, is pushing a broad trans-Atlantic agenda even as his influence wanes in his final months in office. And Brown's public approval has been undermined by rising food and fuel prices, unpopular tax changes and other troubles.

Beyond Iraq, the two leaders will discuss the international effort to halt Iran's nuclear ambitions, Bush's national security adviser Stephen Hadley told reporters traveling with the president on Sunday.

Bush began his day with a bike ride and a church service in Paris, then shifted to London as his weeklong European trip neared its end. Security was tight in London as anti-Bush demonstrators prepared to vent their anger at the U.S. president.

The president got a dash of history and British grandeur on his farewell tour of Europe.

He and his wife, Laura, flew by helicopter to the sweeping lawns of Windsor Castle to visit Queen Elizabeth II. Soldiers in black bearskin hats and red tunics heralded their arrival at the great stone edifice high above the Thames River.

Bush, the queen, Prince Philip and the first lady had tea and strolled through St. George's Hall, a massive, ornate room of red carpet and coats of arms of the Knights of the Garter. They stopped before they entered the grand hall to gaze at an imposing suit of armor once worn by King Henry VIII.

The queen, in a pink floral dress, showed the Bushes through parts of her official residence, which has been a royal home and fortress for more than 900 years. British authorities say it is the largest occupied castle in the world. The president and first lady, who was dressed in a turquoise suit, saw a photo of former President Ronald Reagan riding horses with the queen on the castle grounds in 1982.

Bush was to meet privately with British troops and have a social dinner Sunday evening with British Prime Minister Gordon Brown and his wife, Sarah, at Downing Street. Then, on Monday, breakfast with former British Prime Minister Tony Blair, now an envoy to the international diplomatic quartet on the Middle East. Bush and Brown also planned to travel together to Northern Ireland.

Bush and the British leader were also to discuss Middle East peace, climate change, trade and Northern Ireland governance.

On the day Bush got to London, a British newspaper prominently reported that the president, in an interview earlier in the week, had delivered a warning to Brown about additional reductions of British forces in Iraq. The Observer story said Bush's words amounted to a "stern message" to Brown.

The White House quickly countered, insisting that Bush and Brown remain in accord about Iraq.

"What the president said is what the president has been saying and Prime Minister Brown has been saying from the very beginning," Hadley told reporters traveling on Air Force One. "Obviously, we all want to begin to bring the troops home, but we all recognize we can only do that as they succeed."

Brown's Downing Street office concurred, saying it was not British policy to set "arbitrary timetables."

In the White House transcript of the interview, Bush said that there should be "no definitive timetable" for troop withdrawals, and that the reduction of forces should be based only on success in improving security. He said that, from his perspective, that's how Brown was approaching the matter, too.

Beyond Iraq, the prospect of a nuclear-armed Iran has loomed over Bush's entire trip.

The United States and other Western nations fear Iran's pursuit of uranium enrichment is intended for nuclear weaponry that could destabilize the Middle East and the broader world. Iran insists it is only aiming to develop nuclear energy, and it has rebuffed international efforts to halt enrichment.

In Northern Ireland, where Protestants and Catholics have a power-sharing agreement after years of violent conflict, Bush plans to discuss the overdue devolution of police and justice responsibilities to Northern Ireland authorities. Bush will encourage the setting of a firm date for this, Hadley said.

The quick stop in Northern Ireland on Monday will be the last on Bush's trip. He has also been to Slovenia, Germany, Italy and France.

Earlier, in Paris, Bush made a point again to note he was concerned about the record flooding in Iowa and other parts of the Midwest.

The president was briefed on the flooding while he was in Paris, as he was during other stops of his trip. He was assured that federal agencies were making plans to help those affected by the high water, White House press secretary Dana Perino said.

Bush and his wife attended a service at the American Cathedral of the Holy Trinity, an Episcopal-Anglican church near the Eiffel Tower. He said afterward, "Laura and I had the joy of worshipping here in Paris."

Bush also wished a happy Father's Day to the dads in America — including his own, the first President Bush.

Before church, Bush took an early morning bike ride at the Parc de St. Cloud, a former French estate on a hillside. The air was brisk and the sky was overcast with gray clouds as Bush pedaled for about an hour through the green, wooded park.