LONDON — Senator McCain yesterday conceded that the British public is “frustrated” over the war in Iraq, but warned that the battle is not won despite recent improvements in the security situation.

“The fact is, Al Qaeda is on the run. They are not defeated; they are not defeated. And we’re going to have to continue training Iraqi military and doing what we’ve been doing,” Mr. McCain said after meeting with the British prime minister, Gordon Brown, in the midst of a foreign policy swing through the Middle East and Europe.

The meeting was seen in Britain as a chance to build bridges with an American presidential hopeful who in the past has been critical of Britain’s troop drawdown in southern Iraq.

Mr. McCain was not openly chastising in his public remarks, instead expressing gratitude for Britain’s contribution to the war effort. But there are growing signs of doubt in London about how fast Mr. Brown might be able to withdraw troops. Britain plans to begin reducing its force from the present level of 4,100 soldiers toward the new target of 2,500 troops this spring.

“There’s a huge amount of progress still to be made in Basra, and without a transformation of the political scene in Basra and a transformation of the Iraqi police, the goal of economic rebirth of Basra, and therefore of Iraq as a whole … will be difficult to achieve, and it is certainly unfulfilled at the moment,” the chairman of Parliament’s select defense committee, James Arbuthnot, told foreign reporters this week ahead of Mr. McCain’s visit.

He said Mr. Brown’s announcement in October of the troop withdrawal left “leeway” for enough delay to ensure that remaining troops are sufficient to defend themselves and train Iraqi police and army forces.

“We’re nowhere near 2,500 now, and quite when we will get there is intended to be left vague, clearly,” he said.

Mr. McCain last month was quoted in Britain’s Daily Telegraph as saying that the British decision to pull back to a single base at Basra airport was premature.

“Obviously I would like to have seen them stay longer and larger. At the time, I didn’t think it was a good idea, but I understood the domestic British political situation,” Mr. McCain said then.

Yesterday he declined to be drawn out further despite persistent questioning.

“I fully appreciate that British public opinion has been frustrated by sometimes a lack of progress in both areas,” he said, referring to Iraq and Afghanistan. “But all I can do is express my gratitude to the British government and people, especially the brave young people who are serving.”

Mr. McCain also would not lay out distinctions between his own foreign policy and that of President Bush, emphasizing that his trip was not as a candidate but as part of a Senate Armed Services Committee delegation, with Senator Lieberman of Connecticut, an independent who caucuses with the Democrats, and Senator Graham, a Republican of South Carolina.

Later in the day, Mr. McCain briefly put back on his campaigning hat for a $1,000-a-plate fundraiser for Americans living in Britain at the elegant Spencer House, the only 18th-century private palace surviving in London, built by an ancestor of the late Princess Diana.

His official meetings also included David Cameron, Britain’s opposition Conservative Party leader, and Stavros Dimas, the E.U. environment commissioner. Establishing America as a leader in slowing climate change has been a priority for Mr. McCain, and he said the issue was an important part of his talks with the British prime minister.